Abstract Isotopies and autotopies of n -ary groups are described. As a consequence, we obtain various characterizations the group automorphisms groups. We also determine number given group.

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free met...

A group G (with additively written, not necessarily commutative group operation and neutral element 0) is called an H-group if there is a certain system Cl of w-ary algebraic operations (for certain natural numbers n) besides the addition such that for each w-ary operation OJEQ the condition 00... 0w = 0 (with n zeros on the left side) is satisfied. An important concept is that of an Q-ideal in...

Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algoŽ . rit...

The purpose of this paper is to enumerate various classes of cyclically colored m-gonal plane cacti, called m-ary cacti. This combinatorial problem is motivated by the topological classiication of complex polynomials having at most m critical values, studied by Zvonkin and others. We obtain explicit formulae for both labelled and unlabelled m-ary cacti, according to i) the number of polygons, i...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

Fuzzy rough n-ary subhypergroups are introduced and characterized.

By means of Hall's Marriage Theorem, a class of q-ary codes are obtained through block designs based on group divisible association schemes with two associate classes. If these block designs are further semiframes, another class of q-ary codes are also constructed. @ 1999 Elsevier Science B.V. All rights reserved