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Results tagged with gr.group-theory
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user 4701
Questions about the branch of algebra that deals with groups.
3
votes
1
answer
1k
views
What is the smallest $n$ such that $G\le S_n$? [duplicate]
Possible Duplicates:
Smallest permutation representation of a finite group?
Smallest n for which G embeds in $S_n$?
Cayley's theorem says that every finite group, $G$ can be thought of as a …
- 1,049
5
votes
2
answers
567
views
When is $\mathbb{G}_m(R)$ enough to determine $R$?
Say I have a ring, $R$, with 1 which I consider my universe, and I know its group of units $G=\mathbb{G}_m(R)$. Then given a subgroup, $H\le G$, can I determine if there is there a subring $S_H$ such …
- 1,049
2
votes
2
answers
1k
views
Place stabilizers for the absolute Galois Group
Fix an algebraic closure, $\overline{\mathbb{Q}}$ for the rationals and consider the set, $B_p$, of all places of $\overline{\mathbb{Q}}$ over a fixed (possibly infinite) prime, $p$, of $\mathbb{Q}$. …
- 1,049
9
votes
2
answers
1k
views
Is it known if the absolute Galois group is "divisible"?
The definitions of a divisible group that I have seen all seem to assume abelian is an a priori property of the group. My question is as to whether or not it is known that--given a non-torsion element …
- 1,049