On the structure of generalized Hamiltonian groups View Full Text


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Article Info

DATE

2000-11

AUTHORS

L.-C. Kappe, D.M. Reboli

ABSTRACT

We consider the characteristic subgroup CS(G), generated by the nonnormal cyclic subgroups of the group G. A group G is called a generalized Dedekind group if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $CS(G)\neq G$\end{document}, and those among them with nontrivial CS(G) are called generalized Hamiltonian groups. Such groups are torsion groups of nilpotency class two. The commutator subgroup is cyclic of p-power or two times p-power order and always contained in CS(G). The quotient G/CS(G) is a locally cyclic p-group. We give an example of an infinite generalized Hamiltonian p-group with G/CS(G) locally cyclic. More... »

PAGES

328-337

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s000130050511

DOI

http://dx.doi.org/10.1007/s000130050511

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1012062451


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