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Question Number 85664 by Jidda28 last updated on 23/Mar/20
Showthatagrouporder100isnotsimple
Commented by mind is power last updated on 24/Mar/20
100=22.52letseesylowTheoremletGgroupoforder100letn5numberof5−SylowGroupwehaven5∣4..1n5=1modd[5]]n5∈{1,2,4}by1n5=1by2⇒H:5−syllowgroupofGisunique⇒HisstablebyconjugategHg−=Hby[definitionofp−SylowGroup⇒Hisnormal⇒GisnotSimpleSinceHissubgroupnormalofG
Commented by Jidda28 last updated on 27/Mar/20
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