Pamela A Ferguson

Induced characters which are multiples of irreducibles

Our statement of Theorem A assumes slightly less than that G is solvable, but we pay a price for that extra generality: we must appeal to the classification of simple groups. Actually, the extra work required in this paper for the sake of not quite assuming that G is solvable is negligible. We merely quote the theorem [2] that groups of central type are solvable. All of the actual use of the list of simple groups and their properties occurs in the proof of that result. It would be nice if no solvability assumption at all were needed in

Strongly self-centralizing Sylow 3-groups

A subgroup M of finite group G is said to be strongly self-centralizing if C,(X) = M for all x E M#. (In particular, M is abelian). A classification of groups in which a Sylow 3-group is strongly self-centralizing follows from work of Herzog (51, Fletcher [3], Ferguson [2], and work of Glauberman on factorizations [4]. The non-abelian simple groups occurring are the infinite family PSJ

Prime characters and primitivity

(~~) (n > 2) and certain examples with just one class of elements of order 3. We apply recent technical results of Sibley [7] to obtain this characterization of PSL2(3n) using character-theoretic methods. Our proof has the advantage of being considerably shorter than previous proofs. The result is:

Algebraic decompositions of commutative association schemes

A natural question, in the character theory of finite groups, is which quasi-primitive characters are actually primitive. A character is said to be quasi-primitive if it is irreducible and its restriction to every normal subgroup is homogeneous. If the group is solvable, T. Berger [9, Th. 11.331 has shown that every quasi-primitive character is actually primitive. If the group is simple, however, every irreducible character is quasi-primitive and may or may not be primitive. The character of degree 5 of Alt(5), for example, is not primitive. It follows that a generalization of Berger’s Theorem to non-solvable groups must include some extra hypotheses which become vacuous when the group is solvable. In this paper we prove the following such theorem, with hypotheses on the chief factors and the character degrees.