• 대한수학회보
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• 제32권2호
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• pp.139-144
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• 1995

Two subgroups U and V of a finite group G are called to be p-conjugate for a prime p if a Sylow p-subgroup of U is conjugate to a Sylow p-subgroup of V. This concept of p-conjugacy also makes sense for some infinite groups with a reasonable Sylow theory.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.285-297
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• 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.

• 대한수학회보
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• 제54권6호
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• pp.2141-2147
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• 2017

Let G be a finite group and m a divisor of ${\mid}G{\mid}$. We prove that G has at least ${\tau}(m)$ cyclic subgroups whose orders divide m, where ${\tau}(m)$ is the number of divisors of m.

• 대한수학회보
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• 제51권4호
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• pp.943-948
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• 2014

Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = $G_0$ < $G_1$ < ${\cdots}$ < $G_t=G$ of G such that, for every i = 1, 2, ${\ldots}$, t, if $G_i/G_{i-1}$ is a p-chief factor, then H either covers or avoids $G_i/G_{i-1}$. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.

• 대한수학회보
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• 제53권1호
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• pp.91-102
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• 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.

• 호남수학학술지
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• 제17권1호
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• 대한수학회보
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• 제26권2호
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• pp.109-114
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• 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.