Question

Number of elements of order $p$ in a (possibly infinite) group

score 99 · Answer 1 · 2021-01-09 18:06:36

99

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Number of elements of order $p$ in a (possibly infinite) group

Published on 09 Jan 2021 - 18:06

score 122 · Answer 2 · 2021-01-13 15:31:24

122

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Let $H, K \lhd G$, then $G = HK \iff G / (H \cap K) \cong G / H \times G / K$

Published on 13 Jan 2021 - 15:31

score 45 · Answer 3 · 2021-01-14 18:24:43

45

Views

Infinite order of a quotient of functions' groups

Published on 14 Jan 2021 - 18:24

score 111 · Answer 4 · 2021-01-20 13:17:15

111

Views

Number of functions from naturals to reals (${\aleph_1}^{\aleph_0}$)

Published on 20 Jan 2021 - 13:17

score 91 · Answer 5 · 2021-01-30 18:18:02

91

Views

Let $|G|$ be infinite. Use normal cores (not Poincaré's Theorem) to prove that if $H, K$ have finite index in $G$, then so does $H\cap K$.

Published on 30 Jan 2021 - 18:18

score 157 · Answer 6 · 2021-01-31 01:49:22

157

Views

Why is $A \rtimes B \simeq \mathbb Z \rtimes \mathbb Z/2\mathbb Z$

Published on 31 Jan 2021 - 1:49

score 68 · Answer 7 · 2021-02-05 15:43:25

68

Views

Say I have some element $g\in G$ such that $g$ is of infinite order. I want to show that $|g|=|\langle g \rangle|$.

Published on 05 Feb 2021 - 15:43

score 37 · Answer 8 · 2021-03-02 18:29:31

37

Views

Intermediate fields of a transcendental field extension

Published on 02 Mar 2021 - 18:29

score 618 · Answer 9 · 2021-03-03 06:52:56

618

Views

Showing that a group has infinite order

Published on 03 Mar 2021 - 6:52

score 98 · Answer 10 · 2021-03-05 00:50:49

98

Views

The equation $2x=a$ has no solution in an infinite additive cyclic group generated by $a$

Published on 05 Mar 2021 - 0:50

score 214 · Answer 11 · 2026-03-27 13:09:00

214

Views

A group such that all its subgroups are finitely generated

Published on 27 Mar 2026 - 13:09

score 197 · Answer 12 · 2021-03-14 15:55:24

197

Views

An infinite group isomorphic to its own automorphism group, but not complete, part 1

Published on 14 Mar 2021 - 15:55

score 70 · Answer 13 · 2021-03-15 03:49:55

70

Views

An infinite group isomorphic to its own automorphism group, but not complete, part 2

Published on 15 Mar 2021 - 3:49

score 174 · Answer 14 · 2021-03-16 09:02:38

174

Views

How to Show Representations of an Infinite Group are not Equivalent?

Published on 16 Mar 2021 - 9:02

score 197 · Answer 15 · 2021-03-21 18:22:38

197

Views

Number of cosets in an infinite group

Published on 21 Mar 2021 - 18:22

List Question

Number of elements of order $p$ in a (possibly infinite) group

Let $H, K \lhd G$, then $G = HK \iff G / (H \cap K) \cong G / H \times G / K$

Infinite order of a quotient of functions' groups

Number of functions from naturals to reals (${\aleph_1}^{\aleph_0}$)

Let $|G|$ be infinite. Use normal cores (not Poincaré's Theorem) to prove that if $H, K$ have finite index in $G$, then so does $H\cap K$.

Why is $A \rtimes B \simeq \mathbb Z \rtimes \mathbb Z/2\mathbb Z$

Say I have some element $g\in G$ such that $g$ is of infinite order. I want to show that $|g|=|\langle g \rangle|$.

Intermediate fields of a transcendental field extension

Showing that a group has infinite order

The equation $2x=a$ has no solution in an infinite additive cyclic group generated by $a$

A group such that all its subgroups are finitely generated

An infinite group isomorphic to its own automorphism group, but not complete, part 1

An infinite group isomorphic to its own automorphism group, but not complete, part 2

How to Show Representations of an Infinite Group are not Equivalent?

Number of cosets in an infinite group

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