The study of symmetry: groups, subgroups, homomorphisms, group actions.

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3
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+50

How many Groups there are on a finite countable set?

Let say cardinality of set S is $n=|S|$. We know that there are $n^{n^2}$ all binary operations on that set. To find out how many groups can be created by this set and by those operations, we need not ...
7
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+100

The largest value of $k$ for $\Bbb{Z}^{k}$ to be embedded in $\mathcal{GL}(n,\Bbb{Z})$.

Reading my course on group theory, I asked my self the following question : Suppose that $\Bbb{Z}^{k}$ can be embedded in $\mathcal{GL}(n,\Bbb{Z})$. What is the largest value of $k$?