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p ‐parts of character degrees
Author(s) -
Lewis Mark L.,
Navarro Gabriel,
Tiep Pham Huu,
TongViet Hung P.
Publication year - 2015
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdv035
Subject(s) - sylow theorems , combinatorics , mathematics , character (mathematics) , finite group , prime (order theory) , bounded function , normal subgroup , group (periodic table) , subgroup , degree (music) , function (biology) , physics , geometry , mathematical analysis , biology , genetics , quantum mechanics , acoustics
We show that if p is an odd prime and G is a finite group satisfying the condition that p 2 divides the degree of no irreducible character of G , then| G : O p( G ) | p ⩽ p 4 , whereO p ( G )is the largest normal p ‐subgroup of G , and if P is a Sylow p ‐subgroup of G , then P ' 'is subnormal in G . Our investigations suggest that if p a is the largest power of p dividing the degrees of irreducible characters of G , then| G : O p( G ) | pis bounded byp f ( a ) , where f ( a ) is a function in a and P ( a + 1 )is subnormal in G .