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TWO APPLICATIONS OF LEWIS’ THEOREM ON CHARACTER DEGREE GRAPHS OF SOLVABLE GROUPS

Liguo He|Yuanhe Zhao|Jianxing Bi
대한수학회 (The Korean Mathematical Society)|2015.03|대한수학회보 (Bulletin of the KMS)|제52권 제2호|pp. 363-366

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참고문헌

키워드

charactersolvable groupfitting subgroupnon-vanishing element
주제분류수학

초록

In this note, we prove Gluck’s conjecture and Isaacs-Navarro- Wolf Conjecture are true for the solvable groups with disconnected graphs by using Lewis’ group structure theorem with respect to the disconnected character degree graphs.

Abstract

In this note, we prove Gluck’s conjecture and Isaacs-Navarro- Wolf Conjecture are true for the solvable groups with disconnected graphs by using Lewis’ group structure theorem with respect to the disconnected character degree graphs.

참고문헌 (13)

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  11. A. Moret´o, "Orbit sizes, character degrees and Sylow subgroups", Adv. Math, 184(1), pp.18~36 (2004)
  12. P. P. P´alfy, "On the character degree graph of solvable groups. II: disconnected graphs", Studia Sci. Math. Hungar, 28, pp.339~355 (2001)
  13. J. P. Zhang, "A note on character degrees of finite solvable groups", Comm. Algebra, 28(9), pp.4249~4258 (2000)

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