• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.285-297
• /
• 1997

We will study the generalization of theorems on the pe-riodic locally - solvable FC-groups to the theorems on the periodic locally-solvable CC-groups. The main theorem is the Theorem A. For the proof the inverse limit of inverse system and topological ap-proch developed by Dixon is useful.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.91-102
• /
• 2016

A chief factor H/K of G is called F-central in G provided $(H/K){\rtimes}(G/C_G(H/K)){\in}{\mathfrak{F}}$. A normal subgroup N of G is said to be ${\pi}{\mathfrak{F}}$-hypercentral in G if either N = 1 or $N{\neq}1$ and every chief factor of G below N of order divisible by at least one prime in ${\pi}$ is $\mathfrak{F}$-central in G. The symbol $Z_{{\pi}{\mathfrak{F}}}(G)$ denotes the ${\pi}{\mathfrak{F}}$-hypercentre of G, that is, the product of all the normal ${\pi}{\mathfrak{F}}$-hypercentral subgroups of G. We say that a subgroup H of G is ${\pi}{\mathfrak{F}}$-embedded in G if there exists a normal subgroup T of G such that HT is s-quasinormal in G and $(H{\cap}T)H_G/H_G{\leq}Z_{{\pi}{\mathfrak{F}}}(G/H_G)$, where $H_G$ is the maximal normal subgroup of G contained in H. In this paper, we use the ${\pi}{\mathfrak{F}}$-embedded subgroups to determine the structures of finite groups. In particular, we give some new characterizations of p-nilpotency and supersolvability of a group.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.109-114
• /
• 1989

This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.