List questions from normal-subgroups

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Having a Normal Sylow 3 subgroup

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275

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When does the set of diagonal matrices over a finite prime field ($GL(n, F)$) form a normal subgroup?

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How to prove its maximality of normal core?

Published on 13 Mar 2014 - 13:52

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Prove that if $H$ is a subgroup of index $2$ in a finite group $G$, then $gH=Hg$ for all $g\in G$

Published on 17 Mar 2014 - 4:30

1k

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Give an example of a non-abelian group G containing a proper normal subgroup N such that $G/N$ is abelian.

Published on 27 Mar 2026 - 17:57

1k

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Prove or disprove the following assertion about a normal subgroup

Published on 26 Mar 2014 - 0:30

62

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Please check my solution.

Published on 28 Mar 2014 - 15:15

112

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Does G necessarily have a subgroup H...

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Conjugacy classes of a subgroup of index 2.

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How to find the order of the elements of $A_4$?

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147

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Prove or disprove.Normal Subgroup.

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Finding all normal subgroups of dihedral group of order eight $D_8$

Published on 31 Mar 2014 - 13:14

3.1k

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Prove the direct product of two subgroups is a subgroup

Published on 26 Mar 2026 - 11:08

183

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What about the index of this subgroup?

Published on 02 Apr 2014 - 9:15

List Question

Normal Subgroups in the Center of a Group

Having a Normal Sylow 3 subgroup

When does the set of diagonal matrices over a finite prime field ($GL(n, F)$) form a normal subgroup?

How to prove its maximality of normal core?

Prove that if $H$ is a subgroup of index $2$ in a finite group $G$, then $gH=Hg$ for all $g\in G$

Give an example of a non-abelian group G containing a proper normal subgroup N such that $G/N$ is abelian.

Prove or disprove the following assertion about a normal subgroup

Please check my solution.

Does G necessarily have a subgroup H...

Conjugacy classes of a subgroup of index 2.

How to find the order of the elements of $A_4$?

Prove or disprove.Normal Subgroup.

Finding all normal subgroups of dihedral group of order eight $D_8$

Prove the direct product of two subgroups is a subgroup

What about the index of this subgroup?

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