This is a survey of the results obtained by K. G lazek and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew elements, constructions of covering groups, classifications and representations of n-ary groups. Some new results are added too.

Given a length m string f over a k-ary alphabet and a positive integer n, we develop eecient algorithms to generate (a) all k-ary strings of length n that have no substring equal to f, (b) all k-ary circular strings of length n that have no substring equal to f, and (c) all k-ary necklaces of length n that have no substring equal to f, where f is an aperiodic necklace. Each of the algorithms ru...

A random m-ary leach tree is constructed from a random permutation of 1, . . . , n. A la of large numbers is obtained for the height Hn of these trees by applying the theory of branching random alks . In particular, it is sho n that Ha/log n y in probability as n ---~ oo, here y = y(m) is a constant depending upon m only. Interestingly, as m ---~ 00 , y(m) is asymptotic to 1/log m, the coeffici...