Principally separated non-separated solvable groups

Abstract

Abstract. If p is a set of primes, a finite group G is called block p-separated if for every two distinct irreducible complex characters a; b A IrrðGÞ there is a prime p A p such that a and b are in di¤erent p-blocks. The group G is called principally p-separated if the above holds whenever b ¼ 1 G . Bessenrodt and Zhang conjectured that if G is a solvable principally pseparated group then G is p-separated. We construct a family of counter-examples to this conjecture.