List questions from quotient-group

Published on 09 Sep 2022 - 17:29

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If $G$ is a group and $N$ is a normal subgroup and if $G=\langle x,y \rangle$ then $G/N = \langle xN,yN \rangle$

Published on 10 Sep 2022 - 13:50

28

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Determination of order of element of a factor group

Published on 11 Sep 2022 - 17:02

68

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Isomorphism of quotient groups: if $G_1 \cong G_2$, then $G_1/K_1 \cong G_2/K_2$?

Published on 14 Sep 2022 - 1:01

129

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Showing $F_X \cong F_Y\implies |X| = |Y|$

Published on 14 Sep 2022 - 13:46

216

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Let $\phi:G_1\to G_2$ isomorphism of groups. Let $H_1\lhd G_1,H_2\lhd G_2$ and suppose that $\phi (H_1) = H_2$. Is true that $G_1/H_1 \cong G_2/H_2$?

Published on 15 Sep 2022 - 13:30

80

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Let $G/H$ be any quotient group and $a^r, a^s$ elements of $G$. If $x \in a^rH \cap a^sH,$ then is $r = s$?

Published on 16 Sep 2022 - 21:06

422

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Properties of cosets; $aH = bH \iff b^{-1}a \in H$.

Published on 25 Sep 2022 - 17:35

101

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Prove that an abelian group has a cyclic quotient

Published on 01 Oct 2022 - 19:28

84

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A smart way of proving that $\langle A/\mathfrak{a}, +, . \rangle$ is a ring.

Published on 01 Oct 2022 - 23:12

38

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About sylow subgroups in $\mathbb{Q} / \mathbb{Z}$

Published on 09 Oct 2022 - 6:06

61

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Quotient groups of the group of differentiable functions over an interval

Published on 09 Oct 2022 - 16:35

152

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Given $N$ char $G$, prove that $N\lt K \lt G$ and $K/N$ char $G/N$ implies $K$ char $G$

Published on 23 Feb 2026 - 7:23

56

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What is the quotient group $G/R(G)$?

Published on 28 Mar 2026 - 12:02

39

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Problem (12.4) in Isaacs Character theory of finite groups

Published on 28 Mar 2026 - 13:41

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Irreducibles in ring of polynomials

If $G$ is a group and $N$ is a normal subgroup and if $G=\langle x,y \rangle$ then $G/N = \langle xN,yN \rangle$

Determination of order of element of a factor group

Isomorphism of quotient groups: if $G_1 \cong G_2$, then $G_1/K_1 \cong G_2/K_2$?

Showing $F_X \cong F_Y\implies |X| = |Y|$

Let $\phi:G_1\to G_2$ isomorphism of groups. Let $H_1\lhd G_1,H_2\lhd G_2$ and suppose that $\phi (H_1) = H_2$. Is true that $G_1/H_1 \cong G_2/H_2$?

Let $G/H$ be any quotient group and $a^r, a^s$ elements of $G$. If $x \in a^rH \cap a^sH,$ then is $r = s$?

Properties of cosets; $aH = bH \iff b^{-1}a \in H$.

Prove that an abelian group has a cyclic quotient

A smart way of proving that $\langle A/\mathfrak{a}, +, . \rangle$ is a ring.

About sylow subgroups in $\mathbb{Q} / \mathbb{Z}$

Quotient groups of the group of differentiable functions over an interval

Given $N$ char $G$, prove that $N\lt K \lt G$ and $K/N$ char $G/N$ implies $K$ char $G$

What is the quotient group $G/R(G)$?

Problem (12.4) in Isaacs Character theory of finite groups

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