Automorphisms of Extensions of ℚ by a Direct Sum of Finitely Many Copies of ℚ View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02

AUTHORS

He Guo Liu, Yu Lei Wang, Ji Ping Zhang

ABSTRACT

Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm). More... »

PAGES

1-9

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10114-018-8113-7

DOI

http://dx.doi.org/10.1007/s10114-018-8113-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110668341


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0601", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biochemistry and Cell Biology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Hubei University", 
          "id": "https://www.grid.ac/institutes/grid.34418.3a", 
          "name": [
            "Department of Mathematics, Hubei University, 430062, Wuhan, P. R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Liu", 
        "givenName": "He Guo", 
        "id": "sg:person.01106315335.15", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01106315335.15"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Department of Mathematics, He\u2019nan University of Technology, 450001, Zhengzhou, P. R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Wang", 
        "givenName": "Yu Lei", 
        "id": "sg:person.011721262635.67", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011721262635.67"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Peking University", 
          "id": "https://www.grid.ac/institutes/grid.11135.37", 
          "name": [
            "The School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zhang", 
        "givenName": "Ji Ping", 
        "id": "sg:person.07364601500.32", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07364601500.32"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-1-4419-8594-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008672834", 
          "https://doi.org/10.1007/978-1-4419-8594-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-8594-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008672834", 
          "https://doi.org/10.1007/978-1-4419-8594-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jabr.2001.8826", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019212586"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11425-009-0151-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028385032", 
          "https://doi.org/10.1007/s11425-009-0151-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11425-009-0151-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028385032", 
          "https://doi.org/10.1007/s11425-009-0151-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s002776300001117x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036556071"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1216/rmj-1972-2-2-159", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064427418"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1360/012010-306", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1065065272"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-02", 
    "datePublishedReg": "2019-02-01", 
    "description": "Let G be an extension of \u211a by a direct sum of r copies of \u211a. (1) If G is abelian, then G is a direct sum of r + 1 copies of \u211a and AutG \u2245 GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial \u211a-group E and m copies of \u211a, where E/\u03b6E is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG\u2032G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G\u2032 of G, and AutG/\u03b6G,\u03b6GG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center \u03b6G of G. Then (i) The extension 1 \u2192 AutG\u2032G \u2192 AutG \u2192 AutG\u2032 \u2192 1 is split; (ii) AutG\u2032G/AutG/\u03b6G,\u03b6GG \u2245 Sp(2n,Q) \u00d7 (GL(m, Q) \u22c9 \u211a(m)); (iii) AutG/\u03b6G,\u03b6GG/InnG \u2245 \u211a(2nm).", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10114-018-8113-7", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040372", 
        "issn": [
          "1439-8516", 
          "1439-7617"
        ], 
        "name": "Acta Mathematica Sinica, English Series", 
        "type": "Periodical"
      }
    ], 
    "name": "Automorphisms of Extensions of \u211a by a Direct Sum of Finitely Many Copies of \u211a", 
    "pagination": "1-9", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "579a059c3373018aa2d9af7f4cbdc317073409e88ef4e578c4bed6e564d0adfa"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10114-018-8113-7"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1110668341"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10114-018-8113-7", 
      "https://app.dimensions.ai/details/publication/pub.1110668341"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:24", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000296_0000000296/records_57234_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs10114-018-8113-7"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-8113-7'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-8113-7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-8113-7'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-8113-7'


 

This table displays all metadata directly associated to this object as RDF triples.

94 TRIPLES      21 PREDICATES      31 URIs      17 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10114-018-8113-7 schema:about anzsrc-for:06
2 anzsrc-for:0601
3 schema:author N0705b253b3a34184b8d63c09c529e1e7
4 schema:citation sg:pub.10.1007/978-1-4419-8594-1
5 sg:pub.10.1007/s11425-009-0151-2
6 https://doi.org/10.1006/jabr.2001.8826
7 https://doi.org/10.1017/s002776300001117x
8 https://doi.org/10.1216/rmj-1972-2-2-159
9 https://doi.org/10.1360/012010-306
10 schema:datePublished 2019-02
11 schema:datePublishedReg 2019-02-01
12 schema:description Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm).
13 schema:genre research_article
14 schema:inLanguage en
15 schema:isAccessibleForFree false
16 schema:isPartOf sg:journal.1040372
17 schema:name Automorphisms of Extensions of ℚ by a Direct Sum of Finitely Many Copies of ℚ
18 schema:pagination 1-9
19 schema:productId N001bd5d1eebe415fbf97f2c5f3f0f67d
20 N1e59d606f53442579f8a8223a063d604
21 Na6ece1189c9b490cb81303afb83bacc0
22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110668341
23 https://doi.org/10.1007/s10114-018-8113-7
24 schema:sdDatePublished 2019-04-11T08:24
25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
26 schema:sdPublisher Naff02555117740d6be8ff5467efab93b
27 schema:url https://link.springer.com/10.1007%2Fs10114-018-8113-7
28 sgo:license sg:explorer/license/
29 sgo:sdDataset articles
30 rdf:type schema:ScholarlyArticle
31 N001bd5d1eebe415fbf97f2c5f3f0f67d schema:name readcube_id
32 schema:value 579a059c3373018aa2d9af7f4cbdc317073409e88ef4e578c4bed6e564d0adfa
33 rdf:type schema:PropertyValue
34 N0705b253b3a34184b8d63c09c529e1e7 rdf:first sg:person.01106315335.15
35 rdf:rest N81c95cfd208f446ca4423910aff578b5
36 N1e59d606f53442579f8a8223a063d604 schema:name doi
37 schema:value 10.1007/s10114-018-8113-7
38 rdf:type schema:PropertyValue
39 N2b7dc9b5fd3a42a2b816f0177e8c5a76 rdf:first sg:person.07364601500.32
40 rdf:rest rdf:nil
41 N81c95cfd208f446ca4423910aff578b5 rdf:first sg:person.011721262635.67
42 rdf:rest N2b7dc9b5fd3a42a2b816f0177e8c5a76
43 Na6ece1189c9b490cb81303afb83bacc0 schema:name dimensions_id
44 schema:value pub.1110668341
45 rdf:type schema:PropertyValue
46 Naff02555117740d6be8ff5467efab93b schema:name Springer Nature - SN SciGraph project
47 rdf:type schema:Organization
48 Nb508bfde54594b3a8374e383e35e1b90 schema:name Department of Mathematics, He’nan University of Technology, 450001, Zhengzhou, P. R. China
49 rdf:type schema:Organization
50 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
51 schema:name Biological Sciences
52 rdf:type schema:DefinedTerm
53 anzsrc-for:0601 schema:inDefinedTermSet anzsrc-for:
54 schema:name Biochemistry and Cell Biology
55 rdf:type schema:DefinedTerm
56 sg:journal.1040372 schema:issn 1439-7617
57 1439-8516
58 schema:name Acta Mathematica Sinica, English Series
59 rdf:type schema:Periodical
60 sg:person.01106315335.15 schema:affiliation https://www.grid.ac/institutes/grid.34418.3a
61 schema:familyName Liu
62 schema:givenName He Guo
63 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01106315335.15
64 rdf:type schema:Person
65 sg:person.011721262635.67 schema:affiliation Nb508bfde54594b3a8374e383e35e1b90
66 schema:familyName Wang
67 schema:givenName Yu Lei
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011721262635.67
69 rdf:type schema:Person
70 sg:person.07364601500.32 schema:affiliation https://www.grid.ac/institutes/grid.11135.37
71 schema:familyName Zhang
72 schema:givenName Ji Ping
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07364601500.32
74 rdf:type schema:Person
75 sg:pub.10.1007/978-1-4419-8594-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008672834
76 https://doi.org/10.1007/978-1-4419-8594-1
77 rdf:type schema:CreativeWork
78 sg:pub.10.1007/s11425-009-0151-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028385032
79 https://doi.org/10.1007/s11425-009-0151-2
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1006/jabr.2001.8826 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019212586
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1017/s002776300001117x schema:sameAs https://app.dimensions.ai/details/publication/pub.1036556071
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1216/rmj-1972-2-2-159 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064427418
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1360/012010-306 schema:sameAs https://app.dimensions.ai/details/publication/pub.1065065272
88 rdf:type schema:CreativeWork
89 https://www.grid.ac/institutes/grid.11135.37 schema:alternateName Peking University
90 schema:name The School of Mathematical Sciences, Peking University, 100871, Beijing, P. R. China
91 rdf:type schema:Organization
92 https://www.grid.ac/institutes/grid.34418.3a schema:alternateName Hubei University
93 schema:name Department of Mathematics, Hubei University, 430062, Wuhan, P. R. China
94 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...