Question

Subgroup of index p in an infinite p-group?

score 65 · Answer 1 · 2026-03-17 10:33:09

65

Views

Subgroup of index p in an infinite p-group?

Published on 17 Mar 2026 - 10:33

score 199 · Answer 2 · 2026-03-22 08:12:31

199

Views

For general $n \in \Bbb N$ , how to determine all groups (both finite and infinite) having exactly $n$ conjugacy classes?

Published on 22 Mar 2026 - 8:12

score 158 · Answer 3 · 2026-03-22 10:34:37

158

Views

Geometrical interpretation of a group

Published on 22 Mar 2026 - 10:34

score 787 · Answer 4 · 2026-03-20 03:14:18

787

Views

Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

Published on 20 Mar 2026 - 3:14

score 424 · Answer 5 · 2026-03-20 02:02:04

424

Views

An infinite polycyclic group has a free abelian normal subgroup

Published on 20 Mar 2026 - 2:02

score 125 · Answer 6 · 2026-03-22 08:15:45

125

Views

Orbits of $X$ under $N\triangleleft G$ are of equal length

Published on 22 Mar 2026 - 8:15

score 706 · Answer 7 · 2026-03-20 04:51:40

706

Views

Infinite case: Let $N$ be a normal subgroup of index m in $G$. Prove that $a^{m}\in N$ for all $a\in G$

Published on 20 Mar 2026 - 4:51

score 417 · Answer 8 · 2026-03-22 08:39:57

417

Views

Show that the infinite cyclic group is not isomorphic to a direct product of two nontrivial cyclic groups.

Published on 22 Mar 2026 - 8:39

score 109 · Answer 9 · 2026-03-20 07:07:08

109

Views

If an infinite group acts freely on two sets then the sets are bijective via an action preserving bijection?

Published on 20 Mar 2026 - 7:07

score 127 · Answer 10 · 2026-03-20 14:43:10

127

Views

If an infinite group $G$ acts freely on two sets of same cardinality $> |G|$, then the sets are bijective via an action preserving bijection?

Published on 20 Mar 2026 - 14:43

score 130 · Answer 11 · 2026-03-20 08:57:58

130

Views

For an infinite group $G$, is the collection of all transitive $G$-sets first order elementary?

Published on 20 Mar 2026 - 8:57

score 61 · Answer 12 · 2026-03-25 02:59:34

61

Views

Does a sub vector space based on $\mathbb{I}$ have an infinite basis

Published on 25 Mar 2026 - 2:59

score 277 · Answer 13 · 2026-03-25 02:58:47

277

Views

The Grigorcuk Group solvable?

Published on 25 Mar 2026 - 2:58

score 147 · Answer 14 · 2026-03-24 22:12:46

147

Views

Conjugacy class with $1$ element in an Infinite Simple Group

Published on 24 Mar 2026 - 22:12

score 208 · Answer 15 · 2026-03-25 03:01:21

208

Views

A group with every non-trivial element having infinite order

Published on 25 Mar 2026 - 3:01

List Question

Subgroup of index p in an infinite p-group?

For general $n \in \Bbb N$ , how to determine all groups (both finite and infinite) having exactly $n$ conjugacy classes?

Geometrical interpretation of a group

Is there a good example of a subgroup of an infinitely generated abelian group that is not isomorphic to a quotient of that group?

An infinite polycyclic group has a free abelian normal subgroup

Orbits of $X$ under $N\triangleleft G$ are of equal length

Infinite case: Let $N$ be a normal subgroup of index m in $G$. Prove that $a^{m}\in N$ for all $a\in G$

Show that the infinite cyclic group is not isomorphic to a direct product of two nontrivial cyclic groups.

If an infinite group acts freely on two sets then the sets are bijective via an action preserving bijection?

If an infinite group $G$ acts freely on two sets of same cardinality $> |G|$, then the sets are bijective via an action preserving bijection?

For an infinite group $G$, is the collection of all transitive $G$-sets first order elementary?

Does a sub vector space based on $\mathbb{I}$ have an infinite basis

The Grigorcuk Group solvable?

Conjugacy class with $1$ element in an Infinite Simple Group

A group with every non-trivial element having infinite order

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