# Questions tagged [free-product]

In mathematics, specifically group theory, the free product is an operation that takes two groups $G$ and $H$ and constructs a new group $G\ast H$. The result contains both $G$ and $H$ as subgroups, is generated by the elements of these subgroups, and is the “most general” group having these properties

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### How to compute Lower Central Series by hand for this simple example

Let $G=\langle x,y,z\mid z^2=1\rangle\cong \mathbb{Z}*\mathbb{Z}*\mathbb{Z}/2$. I am interested to compute by hand (or by any other means) the quotient groups $\gamma_n/\gamma_{n+1}$ where $\gamma_n$ ...
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### What is the best book to learn : Free products with amalgamation.

I'm studying groups with Abstact Algebra Grillet, in the free product part, there's a page about amalgamation with two propositions with no proofs, I will be glad if you can recommand a book where ...
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