• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.27-35
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• 2001

We shall deal with ten cases out of 15 distinct almost Bieberbach groups up to Seifert local invariant. In those cases we will show that if G is a finite abelian group acting freely on the standard nilmanifold, then G is cyclic, up to topological conjugacy.

• East Asian mathematical journal
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• v.30 no.3
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• pp.293-302
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• 2014

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.329-333
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• 2022

In this paper we investigate some properties concerning the set of shadowable points for homeomorphisms. Then we show that the almost shadowing property is preserved by a topological conjugacy between homeomorphisms. Also, we give an example to illustrate our results.

• Korean Journal of Mathematics
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• v.1
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• pp.1-6
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• 1993

• Communications of the Korean Mathematical Society
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• v.5 no.1
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• pp.87-90
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• 1990

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.433-446
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• 1999

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. The mapping $theta$ sending a matrix to its transpose-inverse is an auto-mophism of G and therefore we can form the group $G^+$ = G.<$theta$>. In this paper conjugacy classes of elements in $G^+$ -G are found. These classes are closely related to the congruence classes of invert-ible matrices in G.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.773-782
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• 1994

Investigation of the number of representations as well as of projective representations of a finite group has been important object since the early of this century. The numbers are very related to the number of conjugacy classes of G, so that this gives some informations on finite groups and on group characters. A generally well-known fact is that the number of non-equivlaent irreducible representations, which we shall write as n.i.r. of G is less than or equal to the number of conjugacy classes of G, and the equality holds over an algebraically closed field of characteristic not dividing $\mid$G$\mid$. A remarkable result on the numbers due to Reynolds can be stated as follows.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.2
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• pp.98-105
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• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.