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Dergiler / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 3

Non-solvable groups all of whose indices are odd-square-free

Roghayeh HAFEZIEH BALAMAN
Sajjad MAHMOOD ROBATI
Sayfa
746–752
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number.
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Temel Bulgular & Veri:Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number.
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Sonuç & Katkı:In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Given a finite group G and x ∈ G, the class size of x in G is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if G is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of G, which is an answer to the dual of the question mentioned by Huppert in [5].

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Bu Makaleye Atıf Yap

BALAMAN, R. H., ROBATI, S. M. (2022). Non-solvable groups all of whose indices are odd-square-free. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 3, 746–752. https://ajindex.com/articles/607283

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Kaynakça (8)

  1. Babai L, Palfy PP, Saxl J. On the number of p-regular elements in finite simple groups. LMS journal of Computation and Mathematics 2009
  2. doi: 10.1112/S1461157000000036 [2] Chillag D, Herzog M. On the length of the conjugacy classes of finite groups. Journal of Algebra 1990
  3. 131 (1): 110-125. doi: 10.1016/0021-8693(90)90168-N [3] Conway JH, Curtis RT, Norton SP, Parker RA, Wilson RA. ATLAS of finite groups, Clarendon Press, Oxford, 1985. [4] The GAP group, GAP-Groups, Algorithms and Programming, version 4.7.4, 2014. [5] Huppert B. Some simple groups which are determined by the set of their character degrees II. Rendiconti del Seminario Matematico della Università di Padova 2006
  4. Huppert B. Endliche Gruppen, Springer-Verlag, Berlin, 1967. [7] Huppert B, Manz O. Degree-problems I: Square-free character degrees. Archive der Mathematics 1985
  5. doi: 10.1007/BF01270483 [8] Lewis ML. Generalizing a theorem of Huppert and Manz. Journal of Algebra and its Applications 2007
  6. doi: 10.1142/S0219498807002442 [9] Lewis ML, White DL. Non-solvable groups all of whose character degrees are odd-square-free. Communication in Algebra 2011
  7. doi: 10.1080/00927871003652652 [10] Suzuki M. On a class of double transitive groups. Annals of Mathematics 1962
  8. doi: 10.2307/1970423