QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a f...
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| Format: | Article |
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| Language: | English |
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University of Tehran
1998-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31244_e609b7f56af6a239259f8b5c2af6c696.pdf |
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| collection | DOAJ |
| description | By a quasi-permutation matrix we mean a square matrix over the complex field C
with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field Q, and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. In this paper, we will calculate the irreducible modules and characters of metacyclic 2-groups and we also find c(G), q(G) and p(G) for these groups. |
| format | Article |
| id | doaj-art-dcb8dfc079654d80ae880b8a08a5f01f |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 1998-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-dcb8dfc079654d80ae880b8a08a5f01f2025-08-20T03:53:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69141998-09-019331244QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPSBy a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational field Q, and let c(G) be the minimal degree of a faithful representation of G by complex quasi-permutation matrices. In this paper, we will calculate the irreducible modules and characters of metacyclic 2-groups and we also find c(G), q(G) and p(G) for these groups.https://jsciences.ut.ac.ir/article_31244_e609b7f56af6a239259f8b5c2af6c696.pdf |
| spellingShingle | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS Journal of Sciences, Islamic Republic of Iran |
| title | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS |
| title_full | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS |
| title_fullStr | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS |
| title_full_unstemmed | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS |
| title_short | QUASI-PERMUTATION REPRESENTATIONS OF
METACYCLIC 2-GROUPS |
| title_sort | quasi permutation representations of metacyclic 2 groups |
| url | https://jsciences.ut.ac.ir/article_31244_e609b7f56af6a239259f8b5c2af6c696.pdf |