User Giles Gardam

50 votes

What is the current status of the Kaplansky zero-divisor conjecture for group rings?

answered Feb 24, 2021 at 7:56

21 votes

Proving that a countable group is not finitely generated

answered Jul 16, 2022 at 16:05

21 votes

Accepted

Is the number of varieties of groups still unknown?

answered Oct 21 at 10:31

19 votes

Units in the group ring over fours group after Gardam

answered Mar 11, 2021 at 18:25

17 votes

dichotomy in hyperbolic groups

answered May 3, 2023 at 13:52

17 votes

Prove these are not surface groups

answered Feb 4 at 19:58

15 votes

Examples of locally hyperbolic groups

answered Jul 4, 2022 at 9:09

13 votes

Accepted

Dehn functions of finitely presented simple groups

answered May 5, 2023 at 8:17

12 votes

Is It possible to determine whether the given finitely presented group is residually finite with MAGMA or GAP?

answered Jul 22, 2022 at 5:05

12 votes

Does there exist an automorphism of a finitely generated group with periodic points of unbounded period?

answered Dec 17, 2021 at 9:00

11 votes

Accepted

Nonisomorphic central products on the same pair of groups?

answered Feb 12 at 19:35

10 votes

Estimating an upper bound of hyperbolicity constants in Gromov-hyperbolic groups

answered Sep 27 at 9:12

10 votes

Indicability of $\mathrm{Out}(F_n)$

answered Oct 2 at 9:19

10 votes

Accepted

Primitive elements in a free group with trivial projection

answered Jun 16, 2022 at 13:30

9 votes

Accepted

Finite generation of intersections of free subgroups

answered Jun 17, 2022 at 14:16

9 votes

Accepted

Are groups with every proper, non-trivial subgroup infinite cyclic simple?

answered Feb 22, 2022 at 19:46

9 votes

Towards the complex unit conjecture

answered Jan 5 at 15:05

9 votes

Accepted

Subgroup membership problem in simple groups

answered Mar 22, 2023 at 13:09

8 votes

What is the current status of the Kaplansky zero-divisor conjecture for group rings?

answered Oct 4 at 8:30

8 votes

Quasi-isometry groups of metric spaces

answered Jan 27, 2022 at 16:44

7 votes

Centre of group with deficiency at least two (Progress on Murasugi's conjecture)

answered Oct 3 at 9:35

6 votes

Accepted

Examples of Noetherian integral group ring

answered Mar 27 at 15:58

6 votes

Accepted

Existence of m infinite subsets in an arbitrary group such that all products of one element from each (in order) are distinct

answered Jul 4, 2022 at 7:10

6 votes

Accepted

Torsion-free subgroup of affine group

answered Feb 26, 2022 at 14:50

6 votes

Is there a one relator group with property (T)?

answered Mar 19, 2021 at 16:19

5 votes

Accepted

Catalogue of groups with short finite presentations

answered Nov 10, 2022 at 14:37

4 votes

Direct product of free groups in $\mathrm{SL}_3(\mathbb{Z})$

answered Oct 19, 2022 at 11:45

4 votes

Groups whose finite index subgroups of fixed index are isomorphic

answered Dec 6, 2018 at 14:26

4 votes

Automorphisms of virtually abelian groups

answered Nov 5, 2020 at 10:13

4 votes

Examples of IF-groups

answered Feb 23, 2022 at 6:52

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34 Answers

What is the current status of the Kaplansky zero-divisor conjecture for group rings?

Proving that a countable group is not finitely generated

Is the number of varieties of groups still unknown?

Units in the group ring over fours group after Gardam

dichotomy in hyperbolic groups

Prove these are not surface groups

Examples of locally hyperbolic groups

Dehn functions of finitely presented simple groups

Is It possible to determine whether the given finitely presented group is residually finite with MAGMA or GAP?

Does there exist an automorphism of a finitely generated group with periodic points of unbounded period?

Nonisomorphic central products on the same pair of groups?

Estimating an upper bound of hyperbolicity constants in Gromov-hyperbolic groups

Indicability of $\mathrm{Out}(F_n)$

Primitive elements in a free group with trivial projection

Finite generation of intersections of free subgroups

Are groups with every proper, non-trivial subgroup infinite cyclic simple?

Towards the complex unit conjecture

Subgroup membership problem in simple groups

What is the current status of the Kaplansky zero-divisor conjecture for group rings?

Quasi-isometry groups of metric spaces

Centre of group with deficiency at least two (Progress on Murasugi's conjecture)

Examples of Noetherian integral group ring

Existence of m infinite subsets in an arbitrary group such that all products of one element from each (in order) are distinct

Torsion-free subgroup of affine group

Is there a one relator group with property (T)?

Catalogue of groups with short finite presentations

Direct product of free groups in $\mathrm{SL}_3(\mathbb{Z})$

Groups whose finite index subgroups of fixed index are isomorphic

Automorphisms of virtually abelian groups

Examples of IF-groups