RADICAL SUBGROUPS AND THE INDUCTIVE BLOCKWISE ALPERIN WEIGHT CONDITIONS FOR PSp(4)(q)

摘要

We determine explicitly the 2-radical subgroups and their normalizers for the group Sp(4)(q), where q is odd. We then show that the corresponding simple group PSp(4)(q) satisfies the inductive blockwise Alperin weight conditions for the prime 2 and odd primes dividing q(2) - 1. When combined with existing literature, this completes the verification that PSp(4) (q) satisfies the conditions for all primes and all choices of q.