Weak Cayley table groups III: PSL(2,q) |
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| Authors: | Stephen P Humphries Long Nguyen |
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| Institution: | 1. Department of Mathematics, Brigham Young University, Provo, Utah, USAsteve@mathematics.byu.edu;3. Department of Mathematics, Brigham Young University, Provo, Utah, USA |
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| Abstract: | A weak Cayley table isomorphism is a bijection φ:G→H of groups such that φ(xy)～φ(x)φ(y) for all x,y∈G. Here ～ denotes conjugacy. When G = H the set of all weak Cayley table isomorphisms φ:G→G forms a group 𝒲(G) that contains the automorphism group Aut(G) and the inverse map I:G→G,x?x?1. Let 𝒲0(G) = ?Aut(G),I?≤𝒲(G) and say that G has trivial weak Cayley table group if 𝒲(G) = 𝒲0(G). We show that PSL(2,pn) has trivial weak Cayley table group, where p≥5 is a prime and n≥1. |
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| Keywords: | Character table conjugacy class finite group projective special linear group weak Cayley table isomorphism weak Cayley table |
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