List questions from free-groups

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Subgroup of the free group on 3 generators

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Find number of normal subgroups and number of epimorphisms.

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Quotient group of the free group on the alphabet of a string.

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Free groups are torsion-free

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Prove every free group is torsion-free

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Unique factorization of free products of groups satisfying descending chain condition

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Order of $xy$ in various quotients of the free product $G_1 * G_2$, where $x \in G_1, y \in G_2$ are nontrivial

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Proof of Uniqueness of Free Group

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Can free groups on different cardinals be isomorphic in ZF?

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Group of Oriented Edges of a Tiling

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Questions of minimal generating sets of groups.

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Is there a sense in which $(\mathbb{R},+)$ is "free"?

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Why must reduced words in a free group be component-wise equal to be equal?

Published on 25 Mar 2023 - 1:18

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$F_X \cong F_Y \Rightarrow |X| = |Y|$ where is the mistake in this proof

Published on 28 Mar 2023 - 16:02

List Question

Proof of left adjoint for Group to Set

Subgroup of the free group on 3 generators

Find number of normal subgroups and number of epimorphisms.

Quotient group of the free group on the alphabet of a string.

Free groups are torsion-free

Prove every free group is torsion-free

Unique factorization of free products of groups satisfying descending chain condition

Order of $xy$ in various quotients of the free product $G_1 * G_2$, where $x \in G_1, y \in G_2$ are nontrivial

Proof of Uniqueness of Free Group

Can free groups on different cardinals be isomorphic in ZF?

Group of Oriented Edges of a Tiling

Questions of minimal generating sets of groups.

Is there a sense in which $(\mathbb{R},+)$ is "free"?

Why must reduced words in a free group be component-wise equal to be equal?

$F_X \cong F_Y \Rightarrow |X| = |Y|$ where is the mistake in this proof

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