Permutability of subgroups of G×H that are direct products of subgroups of the direct factors View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2001-12

AUTHORS

J. Evan

ABSTRACT

If M and S are two subgroups of a group G, M and Spermute if MS=SM. Furthermore, M is a permutable subgroup of G if M permutes with every subgroup of G. We give necessary and sufficient conditions for M, a subgroup of G, to permute with a subgroup of G×H given that G and H are finite groups. The main part of the paper involves the development of a characterization of permutable subgroups of G×H that are direct products of subgroups of the direct factors; that is, subgroups that are equal to A×B where A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \leqq $\end{document}G and B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \leqq $\end{document}H. More... »

PAGES

449-455

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00000516

DOI

http://dx.doi.org/10.1007/pl00000516

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047072889


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