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

Shitian Liu and Jie Wu

Journal of Mathematics, 2021, vol. 2021, 1-7

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6345386

DOI: 10.1155/2021/6345386

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