List questions from infinite-groups

Published on 25 Mar 2026 - 18:53

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Infinite group has infinitely many subgroups, namely cyclic subgroups.

Published on 30 Nov 2017 - 16:04

59

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Nonconjugate subgroups each containing a conjugate of the other

Published on 05 Dec 2017 - 23:55

480

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Any divisible subgroup of $G$ splits with internal direct product.

Published on 08 Dec 2017 - 13:52

138

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Maximal normal locally nilpotent subgroup in an infinite extension of a Prüfer group

Published on 18 Dec 2017 - 21:29

76

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Does there exist such a group?

Published on 09 Jan 2018 - 6:46

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How do you prove that a group specified by a presentation is infinite?

Published on 27 Mar 2026 - 0:02

339

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An abelian group with $n$ generators and $r(r<n)$ more relations is infinite

Published on 09 Aug 2011 - 5:02

651

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On infinite abelian $p$-group of bounded order

Published on 27 Mar 2026 - 13:41

2.6k

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What is $\operatorname{Aut}(\mathbb{R},+)$?

Published on 01 Mar 2012 - 23:18

1.4k

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Nonabelian infinite nilpotent groups

Published on 25 Mar 2026 - 19:01

14.8k

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An Infinite cyclic group has exactly two generators.

Published on 20 Apr 2012 - 14:41

295

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Finitely generated infinite $p$-group with a unique subgroup of order $p$

Published on 10 Jul 2012 - 8:00

674

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Find the order of a group G from its presentation

Published on 27 Mar 2026 - 0:04

339

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Would you please construct a locally nilpotent group which is not nilpotent?

Published on 25 Mar 2026 - 19:03

List Question

How can group theory explain movement on a hexagonal tiling?

Infinite group has infinitely many subgroups, namely cyclic subgroups.

Nonconjugate subgroups each containing a conjugate of the other

Any divisible subgroup of $G$ splits with internal direct product.

Maximal normal locally nilpotent subgroup in an infinite extension of a Prüfer group

Does there exist such a group?

How do you prove that a group specified by a presentation is infinite?

An abelian group with $n$ generators and $r(r<n)$ more relations is infinite

On infinite abelian $p$-group of bounded order

What is $\operatorname{Aut}(\mathbb{R},+)$?

Nonabelian infinite nilpotent groups

An Infinite cyclic group has exactly two generators.

Finitely generated infinite $p$-group with a unique subgroup of order $p$

Find the order of a group G from its presentation

Would you please construct a locally nilpotent group which is not nilpotent?

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