List questions from free-product

Published on 13 Apr 2026 - 5:45

740

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Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

Published on 09 Apr 2026 - 10:33

234

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If $N$ is the least normal subgroup of $AB$ containing $A$, then $(AB)/N \cong B$.

Published on 17 Apr 2026 - 9:22

25

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Reduced decompositions of elements of an amalgamated sum of monoids

Published on 15 Apr 2026 - 3:01

242

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Let $x^2=y^2=1$ and $xy\neq yx$. There are $\binom{2n}{n}$ expressions of length $2n$ in $x$ and $y$ that are equal to $1$.

Published on 15 Apr 2026 - 20:42

82

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Free Probability and Vandermonde

Published on 13 Apr 2026 - 15:10

55

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What is the correct name for a "product function" on a monoid?

Published on 13 Apr 2026 - 7:19

185

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Free groups and free product of groups are isomorphic

Published on 14 Apr 2026 - 16:23

1.1k

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Double torus minus an open disk

Published on 17 Apr 2026 - 6:17

312

Views

Free Lie sum vs free Lie product

Published on 15 Apr 2026 - 19:10

142

Views

An Exercise from Lang's Algebra

Published on 12 Apr 2026 - 10:00

451

Views

In the coproduct of monoids $A\amalg B$, suppose two words have the same suffix in $B$. Can it be cancelled?

Published on 16 Apr 2026 - 8:33

274

Views

The free group $\mathbb{F}_2$ is a subgroup of a free product

Published on 15 Apr 2026 - 2:43

454

Views

When are free products of pairs of groups isomorphic?

Published on 11 Apr 2026 - 22:30

54

Views

Free product of one-element groups

Published on 14 Apr 2026 - 1:38

List Question

Determining whether an element of a free product of cyclic groups is a commutator.

Can a Free product with amalgamation of $\mathbb{Z}*\mathbb{Z}$ be isomorphic to $\mathbb{Z}\times \mathbb{Z}$?

If $N$ is the least normal subgroup of $AB$ containing $A$, then $(AB)/N \cong B$.

Reduced decompositions of elements of an amalgamated sum of monoids

Let $x^2=y^2=1$ and $xy\neq yx$. There are $\binom{2n}{n}$ expressions of length $2n$ in $x$ and $y$ that are equal to $1$.

Free Probability and Vandermonde

What is the correct name for a "product function" on a monoid?

Free groups and free product of groups are isomorphic

Double torus minus an open disk

Free Lie sum vs free Lie product

An Exercise from Lang's Algebra

In the coproduct of monoids $A\amalg B$, suppose two words have the same suffix in $B$. Can it be cancelled?

The free group $\mathbb{F}_2$ is a subgroup of a free product

When are free products of pairs of groups isomorphic?

Free product of one-element groups

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