List questions from p-groups

Published on 25 Nov 2020 - 19:24

123

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Does the direct sum decomposition of a p-group tell you the number of Prüfer subgroups?

Published on 27 Nov 2020 - 0:09

91

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If $G$ is group with $|G|=p^3$, $p$ prime, then $G'=Z(G)$

Published on 23 Feb 2026 - 5:53

120

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If $\theta :G\rightarrow H$ is a surjective homomorphism, then $\theta(\Phi(G))\leq\Phi(H)$.

Published on 25 Mar 2026 - 7:45

36

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When are elements of a p-group independent mod a power of p?

Published on 02 Dec 2020 - 23:19

94

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Does the Prufer p-group contain direct sums of cyclic groups?

Published on 03 Dec 2020 - 5:40

91

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Showing $\Phi(G)=G'G^p$.

Published on 25 Mar 2026 - 7:41

81

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Special groups and special linear groups

Published on 05 Dec 2020 - 16:21

45

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Finite group having a $p$-subgroup has nontrivial center

Published on 17 Dec 2020 - 21:01

79

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Understanding the proof of ${\rm ord}(G)=p^n \Rightarrow Z(G) \neq \{e\}$.

Published on 19 Dec 2020 - 16:53

178

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How does the $p$-group fixed point theorem proof make sense?

Published on 19 Dec 2020 - 18:16

174

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Automorphism group of a non-abelian group is divisible by $p^2$.

Published on 20 Dec 2020 - 2:47

110

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Splitting theorems in finite p-groups

Published on 26 Mar 2026 - 11:05

96

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Show that a subset $X \subseteq G$ generates $G$ if and only if $X+pG$ generates $G$.

Published on 02 Jan 2021 - 9:33

138

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Let $p$ be a prime number and let $G$ be a $p$-group. Then $G$ contains a normal subgroup of order $p^k$ for every nonnegative $k\le r$

Published on 02 Jan 2021 - 17:01

List Question

When are two Abelian p-groups with the same character isomorphic?

Does the direct sum decomposition of a p-group tell you the number of Prüfer subgroups?

If $G$ is group with $|G|=p^3$, $p$ prime, then $G'=Z(G)$

If $\theta :G\rightarrow H$ is a surjective homomorphism, then $\theta(\Phi(G))\leq\Phi(H)$.

When are elements of a p-group independent mod a power of p?

Does the Prufer p-group contain direct sums of cyclic groups?

Showing $\Phi(G)=G'G^p$.

Special groups and special linear groups

Finite group having a $p$-subgroup has nontrivial center

Understanding the proof of ${\rm ord}(G)=p^n \Rightarrow Z(G) \neq \{e\}$.

How does the $p$-group fixed point theorem proof make sense?

Automorphism group of a non-abelian group is divisible by $p^2$.

Splitting theorems in finite p-groups

Show that a subset $X \subseteq G$ generates $G$ if and only if $X+pG$ generates $G$.

Let $p$ be a prime number and let $G$ be a $p$-group. Then $G$ contains a normal subgroup of order $p^k$ for every nonnegative $k\le r$

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