Normal Subgroups of Odd Order Monomial P(a)q(b)-Groups
Loukaki, Maria I.
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https://hdl.handle.net/2142/86785
Description
Title
Normal Subgroups of Odd Order Monomial P(a)q(b)-Groups
Author(s)
Loukaki, Maria I.
Issue Date
2001
Doctoral Committee Chair(s)
Dade, Everett C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
A finite group G is called monomial if every irreducible character of G is induced from a linear character of some subgroup of G. One of the main questions regarding monomial groups is whether or not a normal subgroup N of a monomial group G is itself monomial. In the case that G is a group of even order, it has been proved (Dade, van der Waall) that N need not be monomial. Here we show that, if G is a monomial group of order paq b, where p and q are distinct odd primes, then any normal subgroup N of G is also monomial.
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