List questions from quotient-group

108

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Let $G$ be a group, and $M$, $N$ be normal subgroups such that $M \leq N$. If $G/N \cong G/M$ then need it be true that $N = M$?

Published on 12 Oct 2019 - 17:13

37

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Suppose $F$ is a finitely generated free group, with $M,N \trianglelefteq F$ such that $M \leq N$. If $F/N \cong F/M$ then need we have $N=M$?

Published on 12 Oct 2019 - 17:46

43

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Help with proof about quotient groups

Published on 26 Feb 2026 - 12:36

112

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Quotient group from direct product?

Published on 16 Oct 2019 - 19:48

74

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Let $G$ be a group, $H\le G$, $N\unlhd G$ with $\gcd(|N|, |G:N|)=1$. Show that $H\le N$ iff $|H|$ divides $|N|$

Published on 17 Oct 2019 - 12:28

517

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What Does it Mean for a Subgroup to Have a Finite Index

Published on 25 Mar 2026 - 22:49

102

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cokernel of a map

Published on 25 Mar 2026 - 9:29

127

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Image of irreducible representation of degree 2

Published on 22 Oct 2019 - 3:05

471

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Intuition with the Inverse Quotient Map

Published on 24 Oct 2019 - 15:18

777

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Are Cosets Isomorphic to One Another

Published on 25 Oct 2019 - 2:01

593

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Conjugacy classes of a quotient group

Published on 25 Oct 2019 - 16:15

55

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Show that $A_4 \times Z_3$ does not have a subgroup of order 18

Published on 28 Oct 2019 - 18:50

40

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Group homomorphism between $\mathbb{Z}/n\Bbb Z$ and $\mathbb{Z}$ must be zero

Published on 03 Nov 2019 - 21:45

110

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Finding the quotient of this free abelian group

Published on 06 Nov 2019 - 15:55

337

Views

Prove that if $R/I$ is a field then $I$ is maximal

Published on 10 Nov 2019 - 17:29

List Question

Let $G$ be a group, and $M$, $N$ be normal subgroups such that $M \leq N$. If $G/N \cong G/M$ then need it be true that $N = M$?

Suppose $F$ is a finitely generated free group, with $M,N \trianglelefteq F$ such that $M \leq N$. If $F/N \cong F/M$ then need we have $N=M$?

Help with proof about quotient groups

Quotient group from direct product?

Let $G$ be a group, $H\le G$, $N\unlhd G$ with $\gcd(|N|, |G:N|)=1$. Show that $H\le N$ iff $|H|$ divides $|N|$

What Does it Mean for a Subgroup to Have a Finite Index

cokernel of a map

Image of irreducible representation of degree 2

Intuition with the Inverse Quotient Map

Are Cosets Isomorphic to One Another

Conjugacy classes of a quotient group

Show that $A_4 \times Z_3$ does not have a subgroup of order 18

Group homomorphism between $\mathbb{Z}/n\Bbb Z$ and $\mathbb{Z}$ must be zero

Finding the quotient of this free abelian group

Prove that if $R/I$ is a field then $I$ is maximal

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