On a permutation representation of the Janko group
โ Scribed by Donald Livingstone
- Publisher
- Elsevier Science
- Year
- 1967
- Tongue
- English
- Weight
- 626 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
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## Abstract The topic of this paper is representing permutation groups by connected graphs with proper edge colourings. Every connected graph __G__ with a proper edge colouring ฯ determines a group __A~c~__(__G__, ฯ) of graph automorphisms which preserve the colours of the edges. We characterize pe
A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful ลฝ . permutation representation of G is denoted by p G . The minimal degree of a faithful representation of G by quasi-permutation matric
We give a combinatorial proof of the formula giving the number of representations of an even permutation ฯ in S n as a product of an n-cycle by an (n -2)-cycle, such a number being (nฯ(ฯ ))(n -3)!, where ฯ(ฯ ) is the number of fixed points of ฯ . This proof relies on the fact that any odd permutatio