论文信息 - Skew-morphisms of cyclic p-groups

Skew-morphisms of cyclic p-groups

Abstract Let G be a finite group having a factorisation G = A ⁢ B {G=AB} into subgroups A and B with B cyclic and A ∩ B = 1 A\cap B=1 , and let b be a generator of B. The associated skew-morphism is the bijective mapping f : A → A {f:A\to A} well-defined by the equality b ⁢ a ⁢ B = f ⁢ ( a ) ⁢ B {baB=f(a)B} , where a ∈ A {a\in A} . In this paper, we shall classify all skew-morphisms of cyclic p-groups, where p is an odd prime.

Roman Nedela | István Kovács

[1] M. J. Curran,et al. The automorphism group of a split metacyclic 2-group , 2006 .

[2] Jozef Sirán,et al. Skew-morphisms of regular Cayley maps , 2002, Discret. Math..

[3] Thomas W. Tucker,et al. Regular Cayley maps for finite abelian groups , 2007 .

[4] Roman Nedela,et al. Half-Regular Cayley Maps , 2015, Graphs Comb..

[5] M. J. Curran,et al. The automorphism group of a split metacyclic p-group , 2006 .

[6] Young Soo Kwon,et al. Regular orientable embeddings of complete bipartite graphs , 2005 .

[7] B. Huppert. Über das Produkt von paarweise vertauschbaren zyklischen Gruppen , 1953 .

[8] Robert Jajcay,et al. Powers of Skew-Morphisms , 2014 .

[9] Underwood Dudley. Elementary Number Theory , 1978 .

[10] Shaofei Du,et al. On the skew-morphisms of dihedral groups , 2016 .

[11] Thomas W. Tucker,et al. Cyclic complements and skew morphisms of groups , 2016 .

[12] B. W. King. Presentations of metacyclic groups , 1973, Bulletin of the Australian Mathematical Society.

[13] Roman Nedela,et al. Decomposition of skew-morphisms of cyclic groups , 2011, Ars Math. Contemp..

[14] B. Huppert. Endliche Gruppen I , 1967 .

[15] Thomas W. Tucker,et al. Regular Cayley maps for cyclic groups , 2014 .

[16] Cristina Sarti. Wada dessins associated with finite projective spaces and Frobenius compatibility , 2011, Ars Math. Contemp..