A subgroup H of a given group G is said to be autopermutable, if HH(α) = H(α)H for all α ∈ Aut(G). We also call H a self-autopermutable subgroup of G, when HH(α) = H(α)H implies that H(α) = H. Moreover, G is said to be EAP-group, if every subgroup of G is autopermutable. One notes that if α runs over the inner automorphisms of the group, one obtains the notions of conjugate-permutability, self-...

Since ‘nice’ and ‘interesting’ can hardly be treated as mathematically formulated features, let us discuss the permutability property. We shall explain it in more detail for the classical example of surfaces with constant negative Gaussian curvature (K-surface) with their Bäcklund transformations. Let r : R → R be a K-surface, and r10 and r01 two K-surfaces obtained by Bäcklund transformations ...

The problem of reachability of the states of transition systems is considered hereby. The notions of partial unfolding and permutability of two operators (including the notion of statically permutable operators) are presented. New algorithm for reachability problem in terms of insertion modeling is described. An example of application of such algorithm is considered.