In this paper we study the normalizer decomposition of a compact Lie group G using information fusion system F on maximal discrete p-toral subgroup. We prove that there is an injective map from set conjugacy classes chains F-centric, F-radical subgroups to p-centric, p-stubborn continuous subgroups. The bijection when π0(G) finite p-group. also classifying space chain mod p equivalent correspon...

We characterize the solvable groups without infinite properly ascending chains of non-BFC subgroups and prove that a non-BFC group with a descending chain whose factors are finite or abelian is a Černikov group or has an infinite properly descending chain of non-BFC subgroups.

Critical to our understanding of the immune system diversity is the determination of the number of germ line V genes. The total number of V genes is given by the product: number of subgroups x number of germ line genes per subgroup. Studies of kappa chains and of embryonic DNA indicate 5-10 V genes per subgroup. Statistical analysis of the limited sequence data of mouse kappa chains suggest abo...

in this note we are going to survey several invariants of finite groups related either to their orders or to generating sets or to lattices of subgroups. some relations among these invariants will be exhibited. special attention will be paid to monotonicity of them.

This paper and its sequel [17] deal with a range of questions about the subgroup structure of infinite symmetric groups. Our concern is with such questions as the following. How can an infinite symmetric group be expressed as the union of a chain of proper subgroups? What are the subgroups that supplement the normal subgroups of an infinite symmetric group? What are the maximal proper subgroups...

an ideal orthodontic force system should exert continuous light force. thus, many efforts have been made to improve the memory characteristics of elastomeric chains. the aim of this study was to compare elastomeric chains (ecs) claimed by their manufacturers to offer high memory with traditional ones according to their force-extension diagrams.in this in-vitro study, ecs were divided into six g...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...