• 대한수학회지
• /
• 제41권5호
• /
• pp.913-920
• /
• 2004

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its containing vertex group.

• 대한수학회보
• /
• 제30권2호
• /
• pp.285-293
• /
• 1993

In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

• 대한수학회보
• /
• 제26권2호
• /
• 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.

• 대한수학회지
• /
• 제46권4호
• /
• pp.675-689
• /
• 2009

As a sequel to the papers [2, 3], we will complete our identification of the groups of units of the finite local rings $\mathbb{Z}_4$[X]/($X^k$ + 2t(X), $2X^{\gamma}$) which is the most general type of finite local rings with a single nilpotent generator over $\mathbb{Z}_4$.

• 대한수학회논문집
• /
• 제16권2호
• /
• pp.205-210
• /
• 2001

In this paper we will determine Schur multipliers of some finite p-groups of order p$^4$.

• Journal of applied mathematics & informatics
• /
• 제20권1_2호
• /
• pp.171-180
• /
• 2006

Two infinite classes of special finite groups considered (The group G is special, if G' and Z(G) coincide). Using certain sequences of numbers we give explicit formulas for the Fibonacci lenghts of these classes which involve the well-known Wall numbers k(n).

• Journal of applied mathematics & informatics
• /
• 제16권1_2호
• /
• pp.303-306
• /
• 2004

There are 49 non-metacyclic p-groups of order less than 1000 with trivial Schur multiplier. In this paper we give a list of deficiency zero presentations for these groups.

• 충청수학회지
• /
• 제13권2호
• /
• pp.71-79
• /
• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• 대한수학회보
• /
• 제56권2호
• /
• pp.501-504
• /
• 2019

In this note, we prove that Gluck's conjecture, Isaacs-Navarro-Wolf Conjecture and Taketa's inequality are true for solvable groups whose character graphs having diameter 3.

• 대한수학회지
• /
• 제22권2호
• /
• pp.173-180
• /
• 1985