List questions from free-groups

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Right action induced by free group homomorphism

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Does a finitely generated group $G$, ever act on $G/N$ freely?

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Show that the free group on three generators is a subgroup of the free group on two generators

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Universal Property...The Map is not Well-defined?

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Is this an example of comaximal ideals $I,J$ such that $IJ\not=I\cap J$?

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$p$-completion is pro-$p$ free

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Exact value of exponential growth rate depends on generating set

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Understand the free group universal property applied to $D_n$

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

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Difference between "generating set" and free product?

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Finitely generated nilpotent group is isomorphic to a quotient of the free nilpotent group.

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Example III.3.2(1) of Baumslag's "Topics in Combinatorial Group Theory": proving $F=\operatorname{gp}(1+\xi\mid \xi\in\Xi)$ is free.

Published on 25 Mar 2026 - 12:29

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Growth rate of free nilpotent group of rank $r$ and nilpotency index $s$.

Published on 03 May 2026 - 6:16

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If $g^5 = h^7$ in a free group, then $g$ and $h$ are in a cyclic subgroup

Published on 25 Mar 2026 - 12:28

List Question

An abelian group $G$ is free abelian if and only if satisfies the projective property

Right action induced by free group homomorphism

Does a finitely generated group $G$, ever act on $G/N$ freely?

Show that the free group on three generators is a subgroup of the free group on two generators

Universal Property...The Map is not Well-defined?

Is this an example of comaximal ideals $I,J$ such that $IJ\not=I\cap J$?

$p$-completion is pro-$p$ free

Exact value of exponential growth rate depends on generating set

Understand the free group universal property applied to $D_n$

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

Difference between "generating set" and free product?

Finitely generated nilpotent group is isomorphic to a quotient of the free nilpotent group.

Example III.3.2(1) of Baumslag's "Topics in Combinatorial Group Theory": proving $F=\operatorname{gp}(1+\xi\mid \xi\in\Xi)$ is free.

Growth rate of free nilpotent group of rank $r$ and nilpotency index $s$.

If $g^5 = h^7$ in a free group, then $g$ and $h$ are in a cyclic subgroup

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