Embeddings of minimal non-abelian p-groups

被引:1
|
作者
Abbaspour, Mohammad Hassan [1 ]
Behravesh, Houshang [2 ]
Ghaffarzadeh, Ghodrat [1 ]
机构
[1] Islamic Azad Univ, Khoy Branch, Tehran, Iran
[2] Univ Urmia, Dept Math, Orumiyeh, Iran
关键词
Quasi-permutation representations; Minimal non-abelian p-groups; Character theory; QUASI-PERMUTATION REPRESENTATIONS;
D O I
10.1016/j.amc.2011.01.054
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let p(G) denote the minimal degree of a faithful representation of G by permutation matrices, and let c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices. See [4]. It is easy to see that c(G) is a lower bound for p(G). Behravesh [H. Behravesh, The minimal degree of a faithful quasi-permutation representation of an abelian group, Glasg. Math. J. 39 (1) (1997) 51-57] determined c(G) for every finite abelian group G and also [H. Behravesh, Quasi-permutation representations of p-groups of class 2, J. Lond. Math. Soc. (2) 55 (2) (1997) 251-260] gave the algorithm of c(G) for each finite group G. In this paper, we first improve this algorithm and then determine c(G) and p(G) for an arbitrary minimal non-abelian p-group G. (C) 2011 Elsevier Inc. All rights reserved.
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页码:658 / 661
页数:4
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