The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is induced from a character φ of U with solvable factor group U/ker(φ). Using the classification of finite simple groups, we prove that these groups are also s...

Solvable Graphs (also known as Reachable Graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). In this paper, the properties of Solvable Graphs are investigated, and a new concept in multi agent moti...

An abstract definition of the groups of square-free order is given that leads naturally to a programmable computation of their number. O. Holder's alternative description of the groups of square-free order is incidentally derived. Throughout this paper G will be a group of order h = n^j p;, where Pj > p2 > • • • >p„ are given prime numbers. 0. Holder proved in 1895 that the number of groups of ...

We study left-invariant generalized K\"ahler structures on almost abelian Lie groups, i.e., solvable groups with a codimension-one normal subgroup. In particular, we classify six-dimensional which admit complex structure and establish of those have Hermitian whose fundamental 2-form is $\partial \bar \partial$-closed. obtain classification determine the 6-dimensional compact solvmanifolds admit...

We study properties and the structure of Cartan subgroups in a connected Lie group. obtain characterisation which generalises W\"ustner's theorem for same. show that are same as those centralizers maximal compact radical. Moreover, we describe recipe constructing containing certain nilpotent solvable characterise quotient group modulo closed normal subgroup images ambient also density power map...

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit infinite (but still incomplete) sets of exact (algebraic) solutions. The hamiltonians of these models are hermitian operators of the form H = −∆ +V1(r)+ (s · l)V2(r)+ (...

In groups, an abelian normal subgroup induces congruence. We construct a class of centrally nilpotent Moufang loops containing subloop that does not induce On the other hand, we prove in 6-divisible loops, every congruence solvability adopted from universal-algebraic commutator theory modular varieties is strictly stronger than classical group theory. It open problem whether two notions coincid...

For a maximal subgroup M of a finite group G , the normal index r¡(G : M) is defined to be the order of a chief factor H/K where H is minimal in the set of supplements of M in G . We obtain several results on the normal index of maximal subgroups M of composite index in G with [G : M]p = 1 which imply G to be solvable, supersolvable.

There are strong analogies between groups definable in o-minimal structures and real Lie groups. Nevertheless, unlike the real case, not every definable group has maximal definably compact subgroups. We study definable groups G which are not definably compact showing that they have a unique maximal normal definable torsion-free subgroup N ; the quotient G/N always has maximal definably compact ...

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups G and H. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when G is solvable or H is nilpotent, i...