Question

Property of Normal Subgroups under Special Conditions

score 50 · Answer 1 · 2019-10-11 21:48:00

50

Views

Property of Normal Subgroups under Special Conditions

Published on 11 Oct 2019 - 21:48

score 108 · Answer 2 · 2019-10-12 17:13:12

108

Views

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

score 37 · Answer 3 · 2019-10-12 17:46:21

37

Views

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

score 144 · Answer 4 · 2026-03-28 08:54:49

144

Views

Question about a group-theoretic Chinese remainder theorem and intersections of normal finite-index subgroups

Published on 28 Mar 2026 - 8:54

score 179 · Answer 5 · 2019-10-14 16:58:54

179

Views

Group in which every nonidentity element is of order 2

Published on 14 Oct 2019 - 16:58

score 301 · Answer 6 · 2019-10-14 23:47:50

301

Views

Give an example of a non-abelian group $G$ such that $H = \{a \in G \mid\operatorname{ord}(a) < \infty\}$ is not a subgroup of $G$.

Published on 14 Oct 2019 - 23:47

score 555 · Answer 7 · 2026-03-27 11:49:09

555

Views

How to show that a group of order $380$ always has a normal subgroup of $95$

Published on 27 Mar 2026 - 11:49

score 484 · Answer 8 · 2026-03-25 17:22:26

484

Views

About Weak-Direct Products being Normal Subgroups of the Direct Product

Published on 25 Mar 2026 - 17:22

score 75 · Answer 9 · 2026-03-26 02:57:44

75

Views

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 26 Mar 2026 - 2:57

score 41 · Answer 10 · 2019-10-18 15:20:55

41

Views

Proving a symmetric group is a subgroup

Published on 18 Oct 2019 - 15:20

score 34 · Answer 11 · 2026-03-26 00:58:42

34

Views

Group Theory: Solvable groups and commutators

Published on 26 Mar 2026 - 0:58

score 143 · Answer 12 · 2026-03-25 06:05:38

143

Views

Generalization of Symmetric Group: $S_n$ to ${\bf S'}_n$

Published on 25 Mar 2026 - 6:05

score 60 · Answer 13 · 2019-10-21 16:29:07

60

Views

Transitivity of normality in $H_0 \triangleleft H_1 \triangleleft H_2 \triangleleft H_3$.

Published on 21 Oct 2019 - 16:29

score 132 · Answer 14 · 2026-03-25 18:51:09

132

Views

Semi-Direct product but not a direct products

Published on 25 Mar 2026 - 18:51

score 38 · Answer 15 · 2019-10-22 21:58:04

38

Views

Analogous of Fitting theorem for abelian group is true?

Published on 22 Oct 2019 - 21:58

List Question

Property of Normal Subgroups under Special Conditions

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 $N=M$?

Question about a group-theoretic Chinese remainder theorem and intersections of normal finite-index subgroups

Group in which every nonidentity element is of order 2

Give an example of a non-abelian group $G$ such that $H = \{a \in G \mid\operatorname{ord}(a) < \infty\}$ is not a subgroup of $G$.

How to show that a group of order $380$ always has a normal subgroup of $95$

About Weak-Direct Products being Normal Subgroups of the 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 $|N|$

Proving a symmetric group is a subgroup

Group Theory: Solvable groups and commutators

Generalization of Symmetric Group: $S_n$ to ${\bf S'}_n$

Transitivity of normality in $H_0 \triangleleft H_1 \triangleleft H_2 \triangleleft H_3$.

Semi-Direct product but not a direct products

Analogous of Fitting theorem for abelian group is true?

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