Question

Why aren't all surjective continuous homomorphisms of topological groups open?

score 64 · Answer 1 · 2026-02-23 02:42:16

64

Views

Why aren't all surjective continuous homomorphisms of topological groups open?

Published on 23 Feb 2026 - 2:42

score 70 · Answer 2 · 2026-03-26 11:01:43

70

Views

Quotient of an abelian group by torsion subgroup provides a characteristic free abelian subgroup?

Published on 26 Mar 2026 - 11:01

score 79 · Answer 3 · 2026-03-26 06:30:57

79

Views

A quotient group of a $p$-group is a $p$-group

Published on 26 Mar 2026 - 6:30

score 90 · Answer 4 · 2023-04-11 19:16:47

90

Views

Show that the size of the pre-image $(\psi(x))$ is the same for all $x$. What is this size equal to?

Published on 11 Apr 2023 - 19:16

score 47 · Answer 5 · 2023-04-13 12:58:03

47

Views

Find the quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}$

Published on 13 Apr 2023 - 12:58

score 147 · Answer 6 · 2026-03-26 19:03:59

147

Views

Solvable-by-finite groups

Published on 26 Mar 2026 - 19:03

score 135 · Answer 7 · 2023-04-16 21:46:09

135

Views

If $[G:K] = m$, then prove that $g^m \in K$ for all $g \in G$.

Published on 16 Apr 2023 - 21:46

score 85 · Answer 8 · 2023-04-17 21:48:40

85

Views

$K \leq H_1 \leq H_2 \leq G$, and that $K \trianglelefteq G$ and $H_1 \trianglelefteq H_2$. show that $[H_2 : H_1] = [H_2/K : H_1/K]$.

Published on 17 Apr 2023 - 21:48

score 147 · Answer 9 · 2026-03-26 19:03:06

147

Views

proof that if G is a solvable group then quotient of G is solvable

Published on 26 Mar 2026 - 19:03

score 80 · Answer 10 · 2026-03-26 19:01:02

80

Views

Maximal quotient group of direct product

Published on 26 Mar 2026 - 19:01

score 29 · Answer 11 · 2023-04-29 11:43:23

29

Views

Isomorphic quotient ring implies sum of numerators

Published on 29 Apr 2023 - 11:43

score 177 · Answer 12 · 2023-05-11 20:45:24

177

Views

Confusion about the difference between HN/N and H/N in the second isomorphism theorem

Published on 11 May 2023 - 20:45

score 81 · Answer 13 · 2026-02-23 02:13:49

81

Views

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

Published on 23 Feb 2026 - 2:13

score 104 · Answer 14 · 2023-06-02 16:40:06

104

Views

Show group defined via quotient of matrix $A$'s columns has order $|\det A|$.

Published on 02 Jun 2023 - 16:40

score 150 · Answer 15 · 2023-06-04 17:17:43

150

Views

Existence of a canonical bijection between $G/H \times H/K$ and $G/K$

Published on 04 Jun 2023 - 17:17

List Question

Why aren't all surjective continuous homomorphisms of topological groups open?

Quotient of an abelian group by torsion subgroup provides a characteristic free abelian subgroup?

A quotient group of a $p$-group is a $p$-group

Show that the size of the pre-image $(\psi(x))$ is the same for all $x$. What is this size equal to?

Find the quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}$

Solvable-by-finite groups

If $[G:K] = m$, then prove that $g^m \in K$ for all $g \in G$.

$K \leq H_1 \leq H_2 \leq G$, and that $K \trianglelefteq G$ and $H_1 \trianglelefteq H_2$. show that $[H_2 : H_1] = [H_2/K : H_1/K]$.

proof that if G is a solvable group then quotient of G is solvable

Maximal quotient group of direct product

Isomorphic quotient ring implies sum of numerators

Confusion about the difference between HN/N and H/N in the second isomorphism theorem

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

Show group defined via quotient of matrix $A$'s columns has order $|\det A|$.

Existence of a canonical bijection between $G/H \times H/K$ and $G/K$

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