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Conjectures that solvable groups whose character graphs having diameter 3 satisfy

Qingyun Meng
대한수학회 (The Korean Mathematical Society)|2019.03|대한수학회보 (Bulletin of the KMS)|제56권 제2호|pp. 501-504|DOI 10.4134/BKMS.b180353

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참고문헌

키워드

finite solvable groupscharacter graphsdiameter 3conjectures
주제분류수학

초록

In this note, we prove that Gluck's conjecture, Isaacs-Navarro -Wolf Conjecture and Taketa's inequality are true for solvable groups whose character graphs having diameter 3.

Abstract

In this note, we prove that Gluck's conjecture, Isaacs-Navarro -Wolf Conjecture and Taketa's inequality are true for solvable groups whose character graphs having diameter 3.

참고문헌 (11)

  1. C. Casolo, "Groups whose character degree graph has diameter three", Israel J. Math, 215(2), pp.523~558 (2016)
  2. D. Gluck, "The largest irreducible character degree of a nite group", Canad. J. Math, 37(3), pp.442~451 (1985)
  3. Liguo He, "TWO APPLICATIONS OF LEWIS’ THEOREM ON CHARACTER DEGREE GRAPHS OF SOLVABLE GROUPS", 대한수학회보, 52(2), pp.363~366 (2015), 대한수학회
  4. I. M. Isaacs, "Character Theory of Finite Groups" (1976), Academic Press
  5. M. L. Lewis, "Derived lengths and character degrees", Proc. Amer. Math. Soc, 126(7), pp.1915~1921 (1998)
  6. M. L. Lewis, "Solvable groups whose degree graphs have two connected components", J. Group Theory, 4(3), pp.255~275 (2001)
  7. M. L. Lewis, "A solvable group whose character degree graph has diameter 3", Proc. Amer. Math. Soc, 130(3), pp.625~630 (2002)
  8. M. L. Lewis, "The Taketa problem and character degree graphs with diameter three", Algebr. Represent. Theory, 18(5), pp.1395~1399 (2015)
  9. O. Manz, "On the number of components of a graph related to character degrees", Proc. Amer. Math. Soc, 103(1), pp.31~37 (1988)
  10. P. Palfy, "On the character degree graph of solvable groups. I. Three primes", Period. Math. Hungar, 36(1), pp.61~65 (1998)
  11. C. B. Sass, "Character degree graphs of solvable groups with diameter three", J. Group Theory, 19(6), pp.1097~1127 (2016)

관련 논문AI추천

TWO APPLICATIONS OF LEWIS’ THEOREM ON CHARACTER DEGREE GRAPHS OF SOLVABLE GROUPSJianxing Bi, Liguo He, Yuanhe Zhao대한수학회 · 대한수학회보2015 · 제52권 제2호On the solvability of a finite group by the sum of subgroup ordersMarius Tarnauceanu대한수학회 · 대한수학회보2020 · 제57권 제6호Non-real groups with exactly two conjugacy classes of the same sizeSajjad Mahmood Robati대한수학회 · 대한수학회논문집2019 · 제34권 제1호On minimal non-NSN-groupsGuiyun Chen, Huaguo Shi, Zhangjia Han대한수학회 · 대한수학회지2013 · 제50권 제3호Finite groups which have many normal subgroupsHaipeng Qu, Mingyao Xu, Qinhai Zhang, Xiaoqiang Guo대한수학회 · 대한수학회지2009 · 제46권 제6호Finite $p$-groups whose normal closures of non-normal subgroups have two ordersLifang Wang대한수학회 · 대한수학회지2022 · 제59권 제4호

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