On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers
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 abeli...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6345386 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849413928141979648 |
|---|---|
| author | Shitian Liu |
| author_facet | Shitian Liu |
| author_sort | Shitian Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6aeaa9129f3c43ecbf55561434c0cbb4 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6aeaa9129f3c43ecbf55561434c0cbb42025-08-20T03:34:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/63453866345386On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime PowersShitian Liu0School of Mathematics, Sichuan University of Arts and Science, Dazhou, Sichuan, 635000, ChinaIsaacs, 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.http://dx.doi.org/10.1155/2021/6345386 |
| spellingShingle | Shitian Liu On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers Journal of Mathematics |
| title | On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers |
| title_full | On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers |
| title_fullStr | On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers |
| title_full_unstemmed | On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers |
| title_short | On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers |
| title_sort | on groups whose irreducible character degrees of all proper subgroups are all prime powers |
| url | http://dx.doi.org/10.1155/2021/6345386 |
| work_keys_str_mv | AT shitianliu ongroupswhoseirreduciblecharacterdegreesofallpropersubgroupsareallprimepowers |