We present a theory of Cayley maps, ie, embeddings of Cayley graphs into oriented
surfaces having the same cyclic rotation of generators around each vertex. These maps …

A skew morphism of a finite group 𝐴 is a permutation 𝜑 of 𝐴 fixing the identity element and
for which there is an integer-valued function 𝜋 on 𝐴 such that φ⁢(x⁢ y)= φ⁢(x)⁢ φ π⁢(x)⁢(y) …

An orientably-regular map $ M $ is a 2-cell embedding of a connected graph in a closed,
orientable surface, with the property that the group $\mathrm {Aut}^\textrm {o} M $ of all …

Recently, regular Cayley maps of cyclic groups and dihedral groups have been classified in
[7] and [20], respectively. A nature question is to classify regular Cayley maps of elementary …

A skew-morphism of a finite group G is a permutation σ on G fixing the identity element such
that the product of< σ> with the left regular representation of G forms a permutation group on …

A skew morphism of a group is a generalisation of an automorphism, arising in the context of
regular Cayley maps or of groups expressible as a product AB of subgroups A and B with B …

A skew-morphism φ of a finite group G is a permutation on G such that φ⁢(1)= 1 and φ⁢(g⁢
h)= φ⁢(g)⁢ φ π⁢(g)⁢(h) for all g, h∈ G, where π is a function from G to 𝐙| φ|, called the …

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving
automorphism group G acts regularly on the directed edge set and has a subgroup …

A skew-morphism of a finite group A is a permutation φ on A fixing the identity element, and
for which there exists an integer function π on A such that, for all x, y∈ A, φ⁢(x⁢ y)= φ⁢(x)⁢ …

The concept of a t-balanced Cayley map is a natural generalization of the previously studied
notions of balanced and anti-balanced Cayley maps (the terms coined by [J. Širáň, M …