On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

Jiangtao Shi, Cui Zhang

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Abstract

Let G be a finite group and (G) the set of the numbers of conjugates of noncyclic proper subgroups of G. We prove that (1) if |(G)| ≤ 2, then G is solvable, and (2) G is a nonsolvable group with |(G)| = 3 if and only if G≅PSL(2,5) or PSL(2,13) or SL(2,5) or SL(2,13).
Original languageEnglish
Article number430870
JournalScientific World Journal
Volume2013
Number of pages3
ISSN2356-6140
DOIs
Publication statusPublished - 2013

Bibliographical note

Copyright © 2013 J. Shi and C. Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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