List questions from p-groups

Published on 29 Aug 2019 - 12:44

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Let $G$ be non-abelian, $|G|=p^3$, where $p$ is an odd prime. Show $\exists N\unlhd G$ with $Z(G)<N<G$ and $N\cong\Bbb Z_p \times\Bbb Z_p$.

Published on 07 Sep 2019 - 16:31

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A finite group of order $p^n$ cannot have a center of order $p^{n-1}$

Published on 09 Sep 2019 - 17:38

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Center of $p$-group of maximal class

Published on 12 Sep 2019 - 9:37

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Nilpotency class of any epimorphic image of a p-group of maximal class

Published on 14 Sep 2019 - 7:25

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If $f$ is a homomorphism, does it map $p$-groups to $p$-groups?

Published on 28 Sep 2019 - 3:23

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Sylow subgroups of soluble groups

Published on 16 Mar 2014 - 21:54

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Order and element set of the group with presentation $\langle a,b \;|\; a^9=1, b^3=a^3, [a,b]=a^3\rangle$

Published on 01 Apr 2014 - 13:29

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Subgroups of abelian $p$-groups

Published on 08 Apr 2014 - 11:11

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$\exists a\in G-H$ such that $aHa^{-1}=H$

Published on 19 Apr 2014 - 18:30

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Classify $p$-groups in which all groups of the same order are isomorphic

Published on 13 May 2014 - 17:58

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$|G|=p^3$ non abelian $\Longrightarrow\gamma_2(G)\lneq Z(G)$

Published on 15 May 2014 - 17:27

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Proving group is $p$-group by contradiction

Published on 16 May 2014 - 0:39

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Cauchy's Theorem $\#$ of elements order $p$

Published on 17 May 2014 - 18:56

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A list of conjugacy classes in elementary abelian $p$-group

Published on 19 May 2014 - 7:00

List Question

Subgroups of infinite $p$-group ($p$ is prime)

Let $G$ be non-abelian, $|G|=p^3$, where $p$ is an odd prime. Show $\exists N\unlhd G$ with $Z(G)<N<G$ and $N\cong\Bbb Z_p \times\Bbb Z_p$.

A finite group of order $p^n$ cannot have a center of order $p^{n-1}$

Center of $p$-group of maximal class

Nilpotency class of any epimorphic image of a p-group of maximal class

If $f$ is a homomorphism, does it map $p$-groups to $p$-groups?

Sylow subgroups of soluble groups

Order and element set of the group with presentation $\langle a,b \;|\; a^9=1, b^3=a^3, [a,b]=a^3\rangle$

Subgroups of abelian $p$-groups

$\exists a\in G-H$ such that $aHa^{-1}=H$

Classify $p$-groups in which all groups of the same order are isomorphic

$|G|=p^3$ non abelian $\Longrightarrow\gamma_2(G)\lneq Z(G)$

Proving group is $p$-group by contradiction

Cauchy's Theorem $\#$ of elements order $p$

A list of conjugacy classes in elementary abelian $p$-group

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