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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1016-1104 2345-6914 |