We give a definition of nilpotent association schemes as a generalization of nilpotent groups and investigate their basic properties. Moreover, for a group-like scheme, we characterize the nilpotency by its character products.

In this paper, we have constituted 3-step general Fibonacci sequences in a nilpotent group with exponent p (p is a prime number) and nilpotency class 4 and given formulas to find the α term of the sequence.

Numerically reliable algorithms for the deadbeat control problem, allowing for a trade-off between the size of the feedback gains and the order of nilpotency of the regulated system, are presented.

The present work shows that Cayley automatic groups are semiautomatic and exhibits some further constructions of semiautomatic groups and in particular shows that every finitely generated group of nilpotency class 3 is semiautomatic.

We investigate decidable properties for regular cellular automata. In particular, we show that regularity itself is an undecidable property and that nilpotency, equicontinuity and positively expansiveness became decidable if we restrict to regular cellular automata.

In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.

In this paper, we have studied the properties of associated gyrogroup °G a given group G nilpotency class 3. We proved that if 3 does not divide order G, then ni...