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Results tagged with gr.group-theory
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user 23571
Questions about the branch of algebra that deals with groups.
8
votes
Accepted
Embedding $S_3$ into $Aut(F_2)$
As Tom Goodwillie noted in his comment, $GL(2,\Bbb Z)$ can be identified with $Out(F_2)$, so the question can be rephrased in terms of lifting subgroups of $Out(F_2)$ to $Aut(F_2)$. There is a Realiz …
- 20k
7
votes
Commutator subgroup of $\Gamma(2).$
The commutator subgroup of $SL(2,\mathbb{Z})$ has index 12 and $\Gamma(2)$ has index 6, but $\Gamma(2)$ does not contain the commutator subgroup since the quotient group $SL(2,\mathbb{Z})/\Gamma(2)$ i …
- 20k
13
votes
Accepted
About the proof of Wajnryb's finite presentation of Mod(S)
It is still an open problem to find a short and simple way to derive a finite presentation for the mapping class group. The book by Farb and Margalit (in the recent preliminary version 4.00) gives a c …
- 20k
10
votes
Computing the structure of the group completion of an abelian monoid, how hard can it be?
An ultra-classical example: the failure of unique factorization in algebraic number fields. Here one looks at the multiplicative monoid of nonzero algebraic integers in a finite extension field of $\m …
- 20k