Subgroups of groups of central type

Author:
Kathleen M. Timmer

Journal:
Trans. Amer. Math. Soc. **189** (1974), 133-161

MSC:
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9947-1974-0357574-8

MathSciNet review:
0357574

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a linear character on the center *Z* of a finite group *Z* of a finite group *H*, such that

(1) where the 's are inequivalent irreducible characters on *H* of the same degree, and

(2) if for some and nonnegative integers , then either for all *i* or for all *i, j*.

The object of the paper is to describe finite groups which satisfy conditions (1) and (2) in terms of the multiplication of the group. If *S* is a *p* Sylow subgroup of the group *H*, and , then *H* satisfies conditions (1) and (2) if and only if

(a) consists of elements of order a power of *p* in , and these elements form *p* conjugacy classes of , and

(b) the elements of form *p* conjugacy classes of .

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0357574-8

Keywords:
Character,
representation,
group of central type,
character of large degree,
projective representation,
projective group algebra

Article copyright:
© Copyright 1974
American Mathematical Society