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On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers

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  • Shitian Liu
  • Jie Wu

Abstract

Isaacs, Passman, and Manz have determined the structure of finite groups whose each degree of the irreducible characters is a prime power. In particular, if G is a nonsolvable group and every character degree of a group G is a prime power, then G is isomorphic to S×A, where S∈A5,PSL28 and A is abelian. In this paper, we change the condition, each character degree of a group G is a prime power, into the condition, each character degree of the proper subgroups of a group is a prime power, and give the structure of almost simple groups whose character degrees of all proper subgroups are all prime powers.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:6345386
    DOI: 10.1155/2021/6345386
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