List questions from infinite-groups

Published on 12 Apr 2017 - 8:18

38

Views

f $G$ is generated by 2 elements, and has a free subgroup $L$ of rank $n+1$, where $|G:L|=n$, then $G$ is free of rank $2$.

Published on 14 Apr 2017 - 12:41

307

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How to prove the Cartesian Product of a set is numerically equivalent to real numbers

Published on 17 Apr 2017 - 21:38

375

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Why is $|\mathbb N | = |\mathbb Z|$?

Published on 18 Apr 2017 - 0:33

77

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Powerset extension of a binary operation of a semigroup

Published on 19 Apr 2017 - 7:22

124

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Intuitive thought about infinities

Published on 26 Apr 2017 - 10:31

129

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Certain property of free products of groups

Published on 25 Mar 2026 - 23:39

203

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How do you describe the following set: $\bigcap_{i=0}^{\infty}(\frac{-1}{i}, \frac{1}{i})$

Published on 11 May 2017 - 2:32

668

Views

Examples of Groups (resp. Rings, Fields, etc.) Which Are Isomorphic to a Proper Subgroup (resp. Subring, Subfield, etc.)

Published on 12 May 2017 - 15:55

159

Views

The cardinality of infinite binary word

Published on 19 May 2017 - 15:27

171

Views

Ulm Invariants of a reduced abelian primary group

Published on 27 Mar 2026 - 8:56

172

Views

Example of a group which is not a free product

Published on 30 May 2017 - 11:18

251

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Commutator of free products of groups

Published on 25 Mar 2026 - 23:38

541

Views

Infinite union of subspaces in a vector space

Published on 05 Jun 2017 - 15:11

327

Views

Growth series for the lamplighter group

Published on 08 Jun 2017 - 1:05

List Question

Probability of selecting an even natural number from the set $\Bbb N$.

f $G$ is generated by 2 elements, and has a free subgroup $L$ of rank $n+1$, where $|G:L|=n$, then $G$ is free of rank $2$.

How to prove the Cartesian Product of a set is numerically equivalent to real numbers

Why is $|\mathbb N | = |\mathbb Z|$?

Powerset extension of a binary operation of a semigroup

Intuitive thought about infinities

Certain property of free products of groups

How do you describe the following set: $\bigcap_{i=0}^{\infty}(\frac{-1}{i}, \frac{1}{i})$

Examples of Groups (resp. Rings, Fields, etc.) Which Are Isomorphic to a Proper Subgroup (resp. Subring, Subfield, etc.)

The cardinality of infinite binary word

Ulm Invariants of a reduced abelian primary group

Example of a group which is not a free product

Commutator of free products of groups

Infinite union of subspaces in a vector space

Growth series for the lamplighter group

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