Fixed point free elements of prime order - School of Maths and Stats ...

Priming ConstructionMG 2007Input:• V ⋊ 〈a〉 elusive of degree n,• 〈a〉 irreducible on V with order prime to p,• point stabiliser W ⋊ 〈b〉,• r a prime dividing |a|.Let• V ′ = V}⊕ ·{{· · ⊕ V}, W ′ = W ⊕ V ⊕ · · · ⊕ Vr copies• g = (1, . . . , 1, a)τ where τ = (12 . . . r)Then V ′ ⋊ 〈g〉 acts elusively on the set of right cosets ofW ′ ⋊ 〈(b, . . . , b)〉 with degree rn.