List questions from free-groups

Published on 02 Mar 2013 - 9:45

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Is the free group on an empty set defined?

Published on 21 Mar 2013 - 20:28

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lower central series and basic generators

Published on 28 Mar 2013 - 15:58

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Extending $f: S \rightarrow G'$ to $f': G \rightarrow G'$ where $f’$ is a homomorphism

Published on 31 Jul 2020 - 11:03

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If $N \triangleleft G$ is virtually solvable and $G/N$ is virtually infinite cyclic then $G$ is virtually solvable.

Published on 26 Mar 2026 - 8:04

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A question in theory of free groups in algebra

Published on 19 Aug 2020 - 12:33

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one-relator groups which are free-by-cyclic

Published on 27 Mar 2026 - 2:06

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Characterize words in the free group on n letters corresponding to homotopy classes of simple closed curves in the sphere with n+1 punctures.

Published on 28 Aug 2020 - 18:25

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Does the largest free group exists(as a "proper group")?

Published on 01 Sep 2020 - 1:26

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Schreier transversal and a basis for commutator subgroup of $F_3$

Published on 27 Mar 2026 - 3:59

292

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Intuition of characteristic property of the free group

Published on 26 Mar 2026 - 2:56

235

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Lee's definition of free abelian group

Published on 26 Mar 2026 - 21:25

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Question about the computation of a formal power series

Published on 27 Mar 2026 - 19:15

95

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Sufficient conditions for a group to be a free group

Published on 27 Mar 2026 - 3:59

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Difficulty in proving that S_3 is isomorphic to the free group on two letters with the following relation:

Published on 27 Mar 2026 - 3:59

List Question

Question on alphabet of a free group and its generating set

Is the free group on an empty set defined?

lower central series and basic generators

Extending $f: S \rightarrow G'$ to $f': G \rightarrow G'$ where $f’$ is a homomorphism

If $N \triangleleft G$ is virtually solvable and $G/N$ is virtually infinite cyclic then $G$ is virtually solvable.

A question in theory of free groups in algebra

one-relator groups which are free-by-cyclic

Characterize words in the free group on n letters corresponding to homotopy classes of simple closed curves in the sphere with n+1 punctures.

Does the largest free group exists(as a "proper group")?

Schreier transversal and a basis for commutator subgroup of $F_3$

Intuition of characteristic property of the free group

Lee's definition of free abelian group

Question about the computation of a formal power series

Sufficient conditions for a group to be a free group

Difficulty in proving that S_3 is isomorphic to the free group on two letters with the following relation:

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