Complex group algebras of the direct product of non-isomorphic Suzuki groups

摘要

In this paper, prove that the direct product Sz(q(1)) x Sz(q(2)) x center dot center dot center dot x Sz(q(k)), where q(i) = 2(2ni+1) >= 8 are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product Sz(2(P1)) x Sz(2(p2)) x center dot center dot center dot x Sz(2(Pk)), where p(i)'s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.