In:
Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP), Vol. 162, No. 2 ( 2017-03), p. 353-365
Abstract:
The classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p , then G has a normal Sylow p -subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem.
Type of Medium:
Online Resource
ISSN:
0305-0041
,
1469-8064
DOI:
10.1017/S0305004116000669
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2017
detail.hit.zdb_id:
1483586-1
detail.hit.zdb_id:
209201-3
SSG:
17,1
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