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Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers

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  • Shitian Liu
  • Xingzheng Tang

Abstract

Huppert and Manz have determined the nonsolvable groups whose character degrees are products of at most two prime numbers. In this paper, we change the condition from “degrees of a group are products of at most two prime divisors” to “degrees of all proper groups of a group are products of at most two prime divisors” and determine the structure of finite groups with such condition.

Suggested Citation

  • Shitian Liu & Xingzheng Tang, 2022. "Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1455299
    DOI: 10.1155/2022/1455299
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    References listed on IDEAS

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    1. Shitian Liu & Jie Wu, 2021. "On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, June.
    2. Amir Khosravi & Behrooz Khosravi, 2003. "A new characterization of some alternating and symmetric groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-10, January.
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