Graduate Student Colloquium
Ramin Takloo-Bighash
UIC
Minimal permutation representations of finite groups
Abstract: Let G be a finite group. A classical theorem of Cayley asserts that one can
always find an injective homomorphism of G into a permutation group S_n. A
minimal n for which such an injection exists is called the degree of G, and
the associated homomorphism a minimal permutation representation. In this
talk, after explaining a number of classical and new results about minimal
representations, I will explain a new polynomial time algorithm to find
minimal representations of a p-group given the subgroup lattice of the group
- the naive algorithm is exponential time. I will end by describing some
(surprising) applications of the algorithm to the structure theory of
p-groups and a conjecture. This is joint with Ben Elias and Lior Silberman.
The talk will be accessible to anyone with one semester of undergraduate
algebra.
Friday February 15, 2008 at 3:00 PM in SEO 636