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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.
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
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