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Results tagged with finite-groups
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user 4600
Questions on group theory which concern finite groups.
4
votes
The automorphism of a group with a given fixed point set
A necessary condition is that $H $ be closed under any function $f $ that is equivariant under automorphisms $\sigma $ of $G $:
$f(\sigma (x))=\sigma (f (x)) $ (and similarly for functions of several …
- 24.8k
2
votes
The finite subgroups of SU(n)
Just want to point out that an algorithm to answer,
given $n$ and a presentation of a finite group $G$, whether $G$ is isomorphic to a finite subgroup of $SU(n)$,
exists as a consequence of Tarski's T …
- 24.8k
7
votes
Accepted
The exceptional isomorphism between PGL(3,2) and PSL(2,7): geometric origin?
V. Dotsenko's construction, on math.stackexchange:
https://math.stackexchange.com/questions/1401/why-psl-3-mathbb-f-2-cong-psl-2-mathbb-f-7/1450#1450
may fit your requirement "combinatorial mapping …
- 24.8k
13
votes
Accepted
Can any finite lattice be realized as an intermediate subgroups lattice?
This is an open problem. See
Wikipedia article: http://en.m.wikipedia.org/wiki/Finite_lattice_representation_problem
Palfy and Pudlak's result (see open-source description in Palfy's article Interva …
- 24.8k
20
votes
4
answers
2k
views
Cayley graph of $A_5$ with generators $(1,2,3,4,5),(1,4,3,2,5)$
The Cayley graph of $A_5$ with two generators of order 5 seems rather complicated. What is its graph genus (orientable or non-orientable)?
The best I could get by trial and error is an embedding wit …
- 24.8k