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 16 Apr 2026 - 0:09

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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.

Published on 17 Apr 2026 - 14:03

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Normal subgroups in Permutation groups

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Why fully characteristic subgroup is normal?

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A finite normal subgroup is a subset of the center

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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 16 Apr 2026 - 5:28

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

Published on 10 Apr 2026 - 18:37

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Determine subgroup generated by a number

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Prove the solution set is a subgroup under mod 2 addition

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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.

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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 16 Apr 2026 - 9:56

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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