A skew morphism φ of a finite group G is a permutation of G fixing the identity of G and satisfying the property φ(gh)=φ(g)φπ(g)(h)for any g,h∈G,where π is a function from G to { 1,2,…,d1)for the order d of φ.If for any g ∈ G,ir(g)=1,then φ is an automorphism of G.Hence a skew morphism is a generalization of an automorphism.When π(φ(g))=π(g)for any g ∈ G,the skew morphism φ is called a smooth skew morphism.In this paper,we classify all smooth skew morphisms of a kind of maximal class 3-groups which have abelian maximal subgroups.
maximal class 3-groupsmooth skew morphismregular Cayley mapskew morphismmaximal subgroup
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