List questions from infinite-groups

Published on 20 Nov 2015 - 7:28

1k

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Number of elements of order $n$ in an infinite group?

Published on 24 Mar 2026 - 22:01

326

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Is there a standard name for this infinite group?

Published on 24 Mar 2026 - 2:12

437

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Example of an infinite non-normal subgroup $H$ of non-abelian (topological)group $G$.

Published on 26 Mar 2026 - 3:49

204

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Solvable group which has a subgroup that is not finitely-generated

Published on 04 Dec 2015 - 3:05

51

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Is $Y(y)=xy$ a permutation?

Published on 07 Dec 2015 - 20:53

364

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Is there an infinite group that has finite subgroup with finite index?

Published on 26 Mar 2026 - 5:28

345

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Infinite group $G$ with subgroup $H$ such that $xHx^{-1} \subset H$, for some $x \in G$

Published on 04 Jan 2016 - 15:05

81

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Is this group simple?

Published on 24 Mar 2026 - 17:18

634

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Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.

Published on 11 Jan 2016 - 16:56

495

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Which of these groups are isomorphic to each other?

Published on 18 Jan 2016 - 20:27

391

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Is this group index infinite?

Published on 18 Jan 2016 - 21:25

138

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Prove that (possibly) infinite group of all invertible maps of X to itself is not Abelian.

Published on 29 Jan 2016 - 0:26

147

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Baer-Specker group versus free abelian group generated by an uncountable set

Published on 29 Jan 2016 - 1:38

1.4k

Views

Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?

Published on 02 Feb 2016 - 13:36

List Question

Does this proof fail if $H$ is not finitely generated?

Number of elements of order $n$ in an infinite group?

Is there a standard name for this infinite group?

Example of an infinite non-normal subgroup $H$ of non-abelian (topological)group $G$.

Solvable group which has a subgroup that is not finitely-generated

Is $Y(y)=xy$ a permutation?

Is there an infinite group that has finite subgroup with finite index?

Infinite group $G$ with subgroup $H$ such that $xHx^{-1} \subset H$, for some $x \in G$

Is this group simple?

Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.

Which of these groups are isomorphic to each other?

Is this group index infinite?

Prove that (possibly) infinite group of all invertible maps of X to itself is not Abelian.

Baer-Specker group versus free abelian group generated by an uncountable set

Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?

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