List questions from normal-subgroups

Published on 25 Feb 2016 - 8:41

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Let a finite group $G$ have $n (>0)$ elements of order $p$ (a prime). If the Sylow $p$-subgroup of $G$ is normal, then does $p$ divide $n+1$?

Published on 30 Mar 2026 - 17:09

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Two Subnormal subgroups with index of one and order of other relatively prime

Published on 26 Feb 2016 - 11:29

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$ G=H_1\times ... \times H_k $ and $ K \unlhd G.$ Then If $K$ is not contained in $Z(G)$, there exists $i$ such that $K\cap H_i \neq \{e\}$

Published on 28 Feb 2016 - 18:19

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Intersection of is the kernel of a homomorphism/representation.

Published on 01 Apr 2026 - 9:54

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Homomorphism and irreducibility

Published on 01 Mar 2016 - 2:15

105

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Question about normal subgroups.

Published on 01 Mar 2016 - 22:20

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Let $G$ be a group of order $120$, let $H≤G$ with $|H|=40$. Prove that there exists $K$ such that $K\unlhd G$, $K≤H$, and $|K|≥20$.

Published on 02 Mar 2016 - 5:31

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elements in the product of subgroups in $S_4$

Published on 02 Apr 2026 - 13:12

37

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IF a group G of order 8. Then, it is impossible that |Z(G)| = 4

Published on 03 Mar 2016 - 7:40

825

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A group is isomorphic to the direct product of two subgroups. Conditions for the subgroups to be normal.

Published on 27 Mar 2026 - 14:03

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Can this subgroup be normal with these conditions?

Published on 04 Mar 2016 - 13:20

722

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Does a group action always induce a quotient?

Published on 25 Mar 2026 - 20:38

354

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The group is not simple

Published on 27 Mar 2026 - 10:33

93

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Subgroup of a group of bijections

Published on 11 Mar 2016 - 3:31

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Let a finite group $G$ have $n (>0)$ elements of order $p$ (a prime). If the Sylow $p$-subgroup of $G$ is normal, then does $p$ divide $n+1$?

Two Subnormal subgroups with index of one and order of other relatively prime

$ G=H_1\times ... \times H_k $ and $ K \unlhd G.$ Then If $K$ is not contained in $Z(G)$, there exists $i$ such that $K\cap H_i \neq \{e\}$

Intersection of is the kernel of a homomorphism/representation.

Homomorphism and irreducibility

Question about normal subgroups.

Let $G$ be a group of order $120$, let $H≤G$ with $|H|=40$. Prove that there exists $K$ such that $K\unlhd G$, $K≤H$, and $|K|≥20$.

elements in the product of subgroups in $S_4$

IF a group G of order 8. Then, it is impossible that |Z(G)| = 4

A group is isomorphic to the direct product of two subgroups. Conditions for the subgroups to be normal.

Can this subgroup be normal with these conditions?

Does a group action always induce a quotient?

The group is not simple

Subgroup of a group of bijections

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