List questions from normal-subgroups

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$N$ and $M$ are normal subgroups, whose sizes are coprime. Show $|MN|=|M||N|$

Published on 05 May 2018 - 18:52

471

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Example of Group that is not Internal direct product under weaker condition

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Suppose there is homomorphism from finite group G onto $Z_{10}$ Then G has Normal Subgroup of index 5 and 2.

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Normal subgroups in Permutation groups

Published on 12 May 2018 - 23:47

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Why fully characteristic subgroup is normal?

Published on 14 May 2018 - 21:19

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A finite normal subgroup is a subset of the center

Published on 25 Mar 2026 - 14:34

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If $M, N$ are normal subgroups in a group $G$ with $M \cap N = 1$, then $mn =nm $ for all $m\in M $ and $n\in N $

Published on 21 May 2018 - 18:13

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$H\lhd G$ implies $C_G(h)/C_H(h)$ is cyclic

Published on 22 May 2018 - 13:52

36

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Determine subgroup generated by a number

Published on 25 May 2018 - 15:22

40

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Prove the solution set is a subgroup under mod 2 addition

Published on 29 May 2018 - 15:08

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normal covering and deck transformation

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How to prove that the following subgroup is normal?

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Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

Published on 23 Feb 2026 - 1:22

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If $N$ is a normal subgroup of $G$ and has an index of 12 in $G$, then what can I say about the order of elements in $N$ or in $G$?

Published on 02 Jun 2018 - 14:42

List Question

How to find elements by which 2 elements of $S_n$ are conjugate to each other?

$N$ and $M$ are normal subgroups, whose sizes are coprime. Show $|MN|=|M||N|$

Example of Group that is not Internal direct product under weaker condition

Suppose there is homomorphism from finite group G onto $Z_{10}$ Then G has Normal Subgroup of index 5 and 2.

Normal subgroups in Permutation groups

Why fully characteristic subgroup is normal?

A finite normal subgroup is a subset of the center

If $M, N$ are normal subgroups in a group $G$ with $M \cap N = 1$, then $mn =nm $ for all $m\in M $ and $n\in N $

$H\lhd G$ implies $C_G(h)/C_H(h)$ is cyclic

Determine subgroup generated by a number

Prove the solution set is a subgroup under mod 2 addition

normal covering and deck transformation

How to prove that the following subgroup is normal?

Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

If $N$ is a normal subgroup of $G$ and has an index of 12 in $G$, then what can I say about the order of elements in $N$ or in $G$?

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