List questions from verbal-subgroups

266

Views

Is it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$?

Published on 13 Feb 2019 - 12:23

242

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Does there exist some sort of classification of finite verbally simple groups?

Published on 14 Feb 2019 - 9:14

108

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Does $D_4$ have a verbal subgroup of order 4?

Published on 16 Feb 2019 - 18:48

141

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Large counterexamples to "Non-isomorphic finite groups have verbal subgroups of different order"

Published on 24 Feb 2019 - 20:22

71

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Does there exist a verbally simple group, which is not characteristically simple?

Published on 22 Mar 2019 - 9:39

60

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Does there exist an Artinian verbally simple group, which is not characteristically simple?

Published on 25 Mar 2019 - 15:40

58

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Do all maximal verbal series have the same length?

Published on 28 Mar 2019 - 16:53

82

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Do the quasiverbal subgroups always exist?

Published on 07 Apr 2019 - 10:08

51

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Are upper quasiverbal and lower quasiverbal subgroups always the same subgroup?

Published on 09 Apr 2019 - 16:00

66

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Is there a formula for $[F_n : V_{\{x^3\}}(F_n)]$?

Published on 11 Apr 2019 - 15:59

123

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When Verbal Subgroups are propers

Published on 23 Oct 2014 - 15:56

70

Views

On a n-Engel Verbal Subgroup be perfect

Published on 12 Nov 2014 - 18:54

93

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Is finite verbal subgroup equivalent to finite index of marginal subgroup?

Published on 21 Nov 2019 - 7:13

16

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Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Published on 29 Nov 2019 - 8:14

610

Views

Verbal subgroups of the group of all $2^n$th roots of unity.

Published on 17 Jan 2020 - 21:30

List Question

Is it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$?

Does there exist some sort of classification of finite verbally simple groups?

Does $D_4$ have a verbal subgroup of order 4?

Large counterexamples to "Non-isomorphic finite groups have verbal subgroups of different order"

Does there exist a verbally simple group, which is not characteristically simple?

Does there exist an Artinian verbally simple group, which is not characteristically simple?

Do all maximal verbal series have the same length?

Do the quasiverbal subgroups always exist?

Are upper quasiverbal and lower quasiverbal subgroups always the same subgroup?

Is there a formula for $[F_n : V_{\{x^3\}}(F_n)]$?

When Verbal Subgroups are propers

On a n-Engel Verbal Subgroup be perfect

Is finite verbal subgroup equivalent to finite index of marginal subgroup?

Is there some sort of formula for $[F_n : V_{\{x^4\}}(F_n)]$?

Verbal subgroups of the group of all $2^n$th roots of unity.

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