In this note we give a polynomial time algorithm to compute the order of the centralizer of a given subgroup of a full linear group over a finite field. The method is deterministic if the characteristic of the ground field is small and Las Vegas in the general case. As an application we whow that the verification of the center of a linear group over a finite field belongs to the complexity class AM. This settles a question of L. Babai.
ASJC Scopus subject areas
- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics