List questions from free-groups

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Let $F$ be freely generated by $\{a, b, c\}$. Prove that $F/N$ is free with basis $aN, bN$, where $N$ is the normal subgroup of $F$ generated by $c$

Published on 27 Mar 2026 - 17:52

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Is $\langle S \rangle / \operatorname{nc}(T) \simeq \langle S \setminus T \rangle$, where $T \subseteq S$?

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Defining a map on a subgroup of a free group

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Every free group admits a fixed-point-free involution automorphism

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380

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Finite index non-normal subgroups of free groups.

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Direct product of groups is not the coproduct

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Is the coproduct of any family of groups a free group

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78

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Showing the rank of a group $H$ is precisely the maximal rank $\alpha$ of a sequence of groups.

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Relations from quotient of free product

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100

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Using Kurosh’s Theorem to study elements of $PSL(2, \mathbb{Z})$

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108

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Endomorphism monoid of free group

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List Question

In van Kampen’s theorem, what happens to the loops not in $\pi_1(U_\alpha \cap U_\beta)$?

What is the difference between "a free group generated by A" and "a group generated by A"?

Hom( , ) and Hom_F( , ) and tensor product

Let $F$ be freely generated by $\{a, b, c\}$. Prove that $F/N$ is free with basis $aN, bN$, where $N$ is the normal subgroup of $F$ generated by $c$

Is $\langle S \rangle / \operatorname{nc}(T) \simeq \langle S \setminus T \rangle$, where $T \subseteq S$?

Basis for a free abelian group $F(X)/F(X)'$

Defining a map on a subgroup of a free group

Every free group admits a fixed-point-free involution automorphism

Finite index non-normal subgroups of free groups.

Direct product of groups is not the coproduct

Is the coproduct of any family of groups a free group

Showing the rank of a group $H$ is precisely the maximal rank $\alpha$ of a sequence of groups.

Relations from quotient of free product

Using Kurosh’s Theorem to study elements of $PSL(2, \mathbb{Z})$

Endomorphism monoid of free group

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