List questions from p-groups

Published on 27 Jun 2017 - 11:43

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proving that various descriptions of the subgroup O^p(G) are equivalent

Published on 15 Jul 2017 - 21:18

1.3k

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Let $p$ be an odd prime. Prove that if $P$ is a non-cyclic $p$-group then $P$ contains a normal subgroup $U$ with $U\cong\Bbb Z_p\times\Bbb Z_p$.

Published on 31 Jul 2017 - 13:58

47

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Is a section of a minimal non $P_1$-group a $P_1$-group?

Published on 05 Aug 2017 - 10:09

51

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If $G$ is minimal non $P_1$-group with a maximal subgroup $M \leq G$, then $|\mho_1(M)|\leq p$.

Published on 10 Aug 2017 - 10:57

847

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infinite abelian group where all elements have order 1, 2, or 4

Published on 15 Aug 2017 - 20:41

32

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for $p>2$, If an element $x$ centrilize $\Omega(A)$ where $A\leq P$

Published on 25 Aug 2017 - 16:27

100

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Is there any English version of p transfer theorem of Wielandt?

Published on 29 Aug 2017 - 12:37

704

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Regarding the nilpotency class of finite p-groups

Published on 05 Sep 2017 - 20:50

198

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Intersections of $p$-Sylow subgroups of group of order $p^2q$

Published on 07 Sep 2017 - 22:32

82

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$P_2$-groups are not always $P_3$-groups : a group by Blackburn

Published on 15 Sep 2017 - 14:31

400

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Intersection of Frattini subgroup and center of a finite $p$-group

Published on 19 Sep 2017 - 21:21

263

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Proof of a result on the lower $p$-series

Published on 10 Oct 2017 - 9:03

498

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If G/N is a cyclic group then, [G,G] =[G,N]

Published on 16 Oct 2017 - 14:12

928

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Conjugates of a cyclic subgroup

Published on 18 Oct 2017 - 12:50

List Question

Cyclicity and number of maximal subgroups

proving that various descriptions of the subgroup O^p(G) are equivalent

Let $p$ be an odd prime. Prove that if $P$ is a non-cyclic $p$-group then $P$ contains a normal subgroup $U$ with $U\cong\Bbb Z_p\times\Bbb Z_p$.

Is a section of a minimal non $P_1$-group a $P_1$-group?

If $G$ is minimal non $P_1$-group with a maximal subgroup $M \leq G$, then $|\mho_1(M)|\leq p$.

infinite abelian group where all elements have order 1, 2, or 4

for $p>2$, If an element $x$ centrilize $\Omega(A)$ where $A\leq P$

Is there any English version of p transfer theorem of Wielandt?

Regarding the nilpotency class of finite p-groups

Intersections of $p$-Sylow subgroups of group of order $p^2q$

$P_2$-groups are not always $P_3$-groups : a group by Blackburn

Intersection of Frattini subgroup and center of a finite $p$-group

Proof of a result on the lower $p$-series

If G/N is a cyclic group then, [G,G] =[G,N]

Conjugates of a cyclic subgroup

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