List questions from free-groups

Published on 03 May 2019 - 23:40

221

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Proving that the free abelian group $G$ for the set $\mathbb{N}$ is isomorphic to its product with itself $G \times G$

Published on 13 May 2019 - 1:37

249

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What's the free product of $\Bbb Z/3\Bbb Z *\Bbb Z/3\Bbb Z $?

Published on 25 Mar 2026 - 14:36

319

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Is the free group on two generators generated by two elements as a monoid?

Published on 25 Mar 2026 - 6:08

116

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Why only define word only with finite product of elements?

Published on 04 Jun 2019 - 13:55

607

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Free Groups and Actions on Trees

Published on 19 Jun 2019 - 15:31

96

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Let $F$ be a free group, $H \leq F$ and $[F:H]=n \in \mathbb{N}$. Show that whenever $K \leq F$ then we have $K \cap H \neq 1$

Published on 12 Jul 2019 - 18:55

174

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Free nilpotent group on 2 generators of class 2.

Published on 21 Mar 2026 - 18:20

130

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Elaboration of the proof that "a group is free iff it is isomorphic to $F[\mathscr{A}]$ for some $\mathscr{A}$".

Published on 19 Jul 2019 - 3:57

127

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Prove free groups $\left<a,b \mid ababa = babab\right> \simeq \left<x,\mid x^2 = y^5\right>$.

Published on 19 Jul 2019 - 5:08

401

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Program to find intersection of subgroups of free groups

Published on 25 Mar 2026 - 1:30

99

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How do you minimize a homomorphism of a subset of a group ring?

Published on 25 Mar 2026 - 9:28

101

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Automorphisms of a free group on $S$ is essentially a bijection of $S$ extended homomorphically?

Published on 25 Mar 2026 - 9:39

528

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Formation of the free group on $S$ is a functor

Published on 03 Sep 2019 - 1:35

114

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Are free groups residually simple?

Published on 25 Mar 2026 - 6:31

List Question

Free Groups are ICC Groups

Proving that the free abelian group $G$ for the set $\mathbb{N}$ is isomorphic to its product with itself $G \times G$

What's the free product of $\Bbb Z/3\Bbb Z *\Bbb Z/3\Bbb Z $?

Is the free group on two generators generated by two elements as a monoid?

Why only define word only with finite product of elements?

Free Groups and Actions on Trees

Let $F$ be a free group, $H \leq F$ and $[F:H]=n \in \mathbb{N}$. Show that whenever $K \leq F$ then we have $K \cap H \neq 1$

Free nilpotent group on 2 generators of class 2.

Elaboration of the proof that "a group is free iff it is isomorphic to $F[\mathscr{A}]$ for some $\mathscr{A}$".

Prove free groups $\left<a,b \mid ababa = babab\right> \simeq \left<x,\mid x^2 = y^5\right>$.

Program to find intersection of subgroups of free groups

How do you minimize a homomorphism of a subset of a group ring?

Automorphisms of a free group on $S$ is essentially a bijection of $S$ extended homomorphically?

Formation of the free group on $S$ is a functor

Are free groups residually simple?

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