Normally monomial p-groups

SOME NORMALLY MONOMIAL p-GROUPS OF MAXIMAL CLASS AND LARGE DERIVED LENGTH By L. G. KOVACS AND

1. A group of prime-power order p is obviously nilpotent of class at most m — 1; if it has class precisely m — 1, it is said to be of maximal class. The derived length of a p-group of maximal class is bounded by log2(3p-3) if p is odd and by 2 if p = 2. Indeed, if m ^ 9 p 4 0 , the derived length is at most 3 (Shepherd [6], Leedham-Green and McKay [5].) The question of whether there is an uncon...

Solvability of Generalized Monomial Groups

The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is induced from a character φ of U with solvable factor group U/ker(φ). Using the classification of finite simple groups, we prove that these groups are also s...

Monomial Characters of Finite Groups

An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...

Projective Monomial Curves in P

6 Generic Hecke Algebras for Monomial Groups

In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b, 1, n). The algebra H specializes to the group algebra of G(b, 1, n) and also to an endomorphism algebra of a representation of GLn(Fq) induced from a solvable subgroup. We construct Kazhdan-Lusztig “R-polynomials” for H and show that they may be used to define a partial order on G(b, 1, n). ...