Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers
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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1455299 |
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| author | Shitian Liu Xingzheng Tang |
| author_facet | Shitian Liu Xingzheng Tang |
| author_sort | Shitian Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-87fe8f5de43d4487b71c9103034f51d3 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-87fe8f5de43d4487b71c9103034f51d32025-08-20T02:09:09ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1455299Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime NumbersShitian Liu0Xingzheng Tang1School of MathematicsSchool of MathematicsHuppert 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.http://dx.doi.org/10.1155/2022/1455299 |
| spellingShingle | Shitian Liu Xingzheng Tang Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers Journal of Mathematics |
| title | Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers |
| title_full | Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers |
| title_fullStr | Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers |
| title_full_unstemmed | Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers |
| title_short | Nonsolvable Groups Whose Degrees of All Proper Subgroups Are the Direct Products of at Most Two Prime Numbers |
| title_sort | nonsolvable groups whose degrees of all proper subgroups are the direct products of at most two prime numbers |
| url | http://dx.doi.org/10.1155/2022/1455299 |
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