List questions from free-product

Published on 18 Feb 2020 - 21:05

737

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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 06 Mar 2020 - 10:22

231

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

Published on 01 Apr 2020 - 17:45

22

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Reduced decompositions of elements of an amalgamated sum of monoids

Published on 07 Apr 2020 - 17:04

240

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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 25 Mar 2026 - 12:50

79

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Free Probability and Vandermonde

Published on 14 Apr 2020 - 19:01

52

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

Published on 22 May 2020 - 15:31

182

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Free groups and free product of groups are isomorphic

Published on 31 May 2020 - 13:14

1k

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Double torus minus an open disk

Published on 08 Aug 2016 - 1:04

308

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Free Lie sum vs free Lie product

Published on 30 Aug 2016 - 17:15

138

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An Exercise from Lang's Algebra

Published on 25 Sep 2016 - 13:54

448

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

Published on 23 Feb 2026 - 6:40

271

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

Published on 05 Dec 2016 - 20:45

451

Views

When are free products of pairs of groups isomorphic?

Published on 01 Jan 2017 - 19:18

50

Views

Free product of one-element groups

Published on 15 Feb 2017 - 4:51

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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