The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups

The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups

We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers‎. ‎Insoluble groups which satisfy the one-prime power hypothesis have been classified‎. ‎However it has remained an o...

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Bibliographic Details
Main Author: Julian Brough
Format: Article
Language:English
Published: University of Isfahan 2019-12-01
Series:International Journal of Group Theory
Subjects:
‎Conjugacy classes‎
‎finite groups‎
‎restriction to substructures
Online Access:http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf
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spelling doaj-f52f6e5b244d4e86896be15ff1751ac82020-11-25T00:11:45ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692019-12-01841310.22108/ijgt.2018.110074.147223001The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groupsJulian Brough0Fachgruppe Mathematik und Informatik, BU Wuppertal, Wuppertal, GermanyWe say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers‎. ‎Insoluble groups which satisfy the one-prime power hypothesis have been classified‎. ‎However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups‎. ‎In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups‎.http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf‎Conjugacy classes‎‎finite groups‎‎restriction to substructures
collection DOAJ
language English
format Article
sources DOAJ
author Julian Brough
spellingShingle Julian Brough
The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
International Journal of Group Theory
‎Conjugacy classes‎
‎finite groups‎
‎restriction to substructures
author_facet Julian Brough
author_sort Julian Brough
title The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
title_short The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
title_full The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
title_fullStr The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
title_full_unstemmed The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
title_sort one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups
publisher University of Isfahan
series International Journal of Group Theory
issn 2251-7650
2251-7669
publishDate 2019-12-01
description We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers‎. ‎Insoluble groups which satisfy the one-prime power hypothesis have been classified‎. ‎However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups‎. ‎In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups‎.
topic ‎Conjugacy classes‎
‎finite groups‎
‎restriction to substructures
url http://ijgt.ui.ac.ir/article_23001_d14fcde9b40ecb50266a73a05dc9479a.pdf
work_keys_str_mv AT julianbrough theoneprimepowerhypothesisforconjugacyclassesrestrictedtonormalsubgroupsandquotientgroups
AT julianbrough oneprimepowerhypothesisforconjugacyclassesrestrictedtonormalsubgroupsandquotientgroups
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