# Questions tagged [abstract-algebra]

For questions about groups, rings, fields, vector spaces, modules and other algebraic objects. Associate with related tags like group-theory, ring-theory, modules, etc. to clarify which topic of abstract algebra is most related to your question and help other users when searching.

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### Proving the given $\mathbb R^3/H$ $\cong$ $\mathbb R^2$ where $H$ = {$(y,0,0)|y \in \mathbb R$}

So I am given a group $\mathbb R^3$ and a group $H$ = {$(y,0,0)|y \in \mathbb R$}. I have to prove that that $\mathbb R^3/H$ $\cong$ $\mathbb R^2$. I am not sure how to even begin. My difficulty is ...
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### Prove that $A_n$, the set of even permutations on a set of length n, is a transitive group of transformations on $S=\{1,2,3,…,n\}$

I already know that $S_n$ is a transitive group of transformations on $S=\{1,2,3,...,n\}$. I am sure that it has to be with the fact that $A_n \subset S_n$ but I do not how to proceed.
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### Semigroup and their monogenic semigroup

A subsemigroup $K$ of $S$ is said to be monogenic if $K = \langle a \rangle$ for some $a \in S$ and the order of $a$ is the size of $K$. If the order of $a$ is finite, then after some time power of $a$...
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### What is meaningful product?

Sentence is this. The product of a standard n product and a standard m product is a meaningful product equal to the standard (m+n) product. This sentence is in Thomas W. Hungerford Algebra : Groups ...
### Is $\lim\limits(\prod_{i\leq n} K)\cong\cup_i(\prod_{j\leq i}K)$ true?
Consider a family of $K-$vector spaces $\prod_{i\leq n}K\to\prod_{i\leq n+1}K$ by embedding where embedding is done by identifying the basis $(1,0,\dots,0)\to (1,0,\dots,0,0),...$ and similarly for ...