Reversible logic plays a fundamental role both in ultra-low power electronics and in quantum computing. It is therefore important to have an insight into the structure of the group formed by the reversible logic gates and their cascading into reversible circuits. Such insight is gained from constructing chains of maximal subgroups. The subgroup of control gates plays a prominent role, as it is ...

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, the nilpotent case. It turns out that context, like for finite nilpotency is equivalent to normalizer property or uniqueness of Sylow subgroups, provided maximal normal torsion-free subgroup nilpotent. As consequence, we show decompositions prove Lie group an expansion reals if...

Let G be a finite group with an abelian normal subgroup N . When does N have a unique conjugacy class of complements in G? We consider this question with a focus on subgroups and properties of maximal subgroups. As corollaries we obtain Theorems 1.6 and 1.7 which are closely related to a result by Parker and Rowley on supplements of a nilpotent normal subgroup (Theorem 1 of [3]). Furthermore, w...

A residually finite (profinite) group G is just infinite if every non-trivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining whether a (closed) subgroup H of a just infinite group is itself just infinite. If G is not virtually abelian, we give a description of the just infinite property for normal subgroups in terms of maximal subgroups. In par...

The aim of this paper is basically to study some of the standard properties of the intuitionistic fuzzy subgroups under a crisp map. Also, we study some properties of intuitionistic fuzzy normal subgroups.

Let $G$ be a graph with vertex set $\{1,2,\ldots,n\}$. Its bond lattice, $BL(G)$, is sublattice of the partition lattice. The elements $BL(G)$ are partitions whose blocks induce connected subgraphs $G$.
 In this article, we consider graphs lattice consists only noncrossing partitions. We define family graphs, called triangulation property and show that any two produce isomorphic lattices. ...