Question

Is Lagrange group theorem still valid for infinite groups?

score 121 · Answer 1 · 2023-02-26 10:28:30

121

Views

Is Lagrange group theorem still valid for infinite groups?

Published on 26 Feb 2023 - 10:28

score 225 · Answer 2 · 2023-02-28 02:10:19

225

Views

Proof check: If $G$ is an infinite group, then it has infinite number of subgroups.

Published on 28 Feb 2023 - 2:10

score 157 · Answer 3 · 2023-03-03 15:20:33

157

Views

Which cyclic groups are automorphism groups?

Published on 03 Mar 2023 - 15:20

score 144 · Answer 4 · 2023-03-12 02:53:53

144

Views

What happens if I add an $\omega$th digit to the $p$-adic numbers?

Published on 12 Mar 2023 - 2:53

score 109 · Answer 5 · 2026-03-25 12:54:30

109

Views

Classification of torsion-free nilpotent groups of class 2

Published on 25 Mar 2026 - 12:54

score 50 · Answer 6 · 2023-03-23 16:09:51

50

Views

Prove that there exist equal number of irrational numbers between any 2 rational numbers, when the difference between the 2 rational numbers is same.

Published on 23 Mar 2023 - 16:09

score 535 · Answer 7 · 2023-03-27 10:33:17

535

Views

Infinite Group with all subgroups having finite index

Published on 27 Mar 2023 - 10:33

score 85 · Answer 8 · 2023-03-28 12:32:14

85

Views

Question about "Infinite Group with all subgroups having finite index"

Published on 28 Mar 2023 - 12:32

score 255 · Answer 9 · 2023-04-08 19:53:21

255

Views

Suppose $G$ and $H$ are two countably infinite abelian groups s.t. every nontrivial element of $G\times H$ has order $7$. Then $G\cong H$.

Published on 08 Apr 2023 - 19:53

score 60 · Answer 10 · 2026-03-26 06:29:56

60

Views

Showing that the direct sum is an infinite $p$-group which is not nilpotent.

Published on 26 Mar 2026 - 6:29

score 172 · Answer 11 · 2023-04-21 12:07:53

172

Views

On infinite permutations of a countable set acting on a set: Does a transposition always witness inequality?

Published on 21 Apr 2023 - 12:07

score 79 · Answer 12 · 2023-04-23 09:48:01

79

Views

Index of an infinite cyclic subgroup of a free group of infinite rank is infinite

Published on 23 Apr 2023 - 9:48

score 75 · Answer 13 · 2023-05-03 04:06:26

75

Views

Show that every $x \in G\setminus \{1\}$ and every $H<G$ have infinitely many conjugates for $G$ infinite simple group.

Published on 03 May 2023 - 4:06

score 60 · Answer 14 · 2023-05-03 15:25:51

60

Views

Extending a group to a ring defining a new operator using group automorphisms.

Published on 03 May 2023 - 15:25

score 78 · Answer 15 · 2023-05-04 20:54:07

78

Views

Prove that there are $g_1, g_2, \cdots, g_n \in G$ with $g_i x_1 = x_i$ such that $g_1 H, g_2 H, \cdots, g_n H$ are all the left cosets of $H$ in $G$.

Published on 04 May 2023 - 20:54

List Question

Is Lagrange group theorem still valid for infinite groups?

Proof check: If $G$ is an infinite group, then it has infinite number of subgroups.

Which cyclic groups are automorphism groups?

What happens if I add an $\omega$th digit to the $p$-adic numbers?

Classification of torsion-free nilpotent groups of class 2

Prove that there exist equal number of irrational numbers between any 2 rational numbers, when the difference between the 2 rational numbers is same.

Infinite Group with all subgroups having finite index

Question about "Infinite Group with all subgroups having finite index"

Suppose $G$ and $H$ are two countably infinite abelian groups s.t. every nontrivial element of $G\times H$ has order $7$. Then $G\cong H$.

Showing that the direct sum is an infinite $p$-group which is not nilpotent.

On infinite permutations of a countable set acting on a set: Does a transposition always witness inequality?

Index of an infinite cyclic subgroup of a free group of infinite rank is infinite

Show that every $x \in G\setminus \{1\}$ and every $H<G$ have infinitely many conjugates for $G$ infinite simple group.

Extending a group to a ring defining a new operator using group automorphisms.

Prove that there are $g_1, g_2, \cdots, g_n \in G$ with $g_i x_1 = x_i$ such that $g_1 H, g_2 H, \cdots, g_n H$ are all the left cosets of $H$ in $G$.

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