• 대한수학회보
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• 제51권4호
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• pp.1205-1210
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• 2014

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that $$E/S{\sim_=}G$$ is finite. For a prime p, $\hat{S}=S/S^{\prime}S^p$ may be regarded as an $F_pG$-module via conjugation in E. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

• 대한수학회지
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• 제59권4호
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• pp.805-819
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• 2022

We describe the structure of finite p-groups in which all normal closures of non-normal subgroups have two orders for p > 2.

• 대한수학회보
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• 제42권3호
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• pp.555-561
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• 2005

In this note we give characterizations for certain HNN extensions with central associated subgroups to be residually finite. We then apply our results to HNN extensions of polycyclic-by-finite groups.

• 대한수학회보
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• 제53권5호
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• pp.1395-1399
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• 2016

We will classify the finite barely non-abelian p-groups.

• 대한수학회지
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• 제49권1호
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• pp.201-221
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• 2012

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.403-410
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• 2006

For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G) = n, and primitive n-centralizer if #Cent(G) = #Cent($\frac{G}{Z(G)}$) = n. The first author in [1], characterized the primitive 6-centralizer finite groups. In this paper we continue this problem and characterize the primitive 7-centralizer finite groups. We prove that a finite group G is primitive 7-centralizer if and only if $\frac{G}{Z(G)}{\simeq}D_{10}$ or R, where R is the semidirect product of a cyclic group of order 5 by a cyclic group of order 4 acting faithfully. Also, we compute #Cent(G) for some finite groups, using the structure of G modulu its center.

• 대한수학회논문집
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• 제12권3호
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• pp.521-530
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• 1997

We first prove a criterion for the conjugacy separability of free products with amalgamation where the amalgamated subgroup is not necessarily cyclic. Applying this result, we show that free products of finite number of polycyclic-by-finite groups with central amalgamation are conjugacy separable. We also show that polygonal products of polycyclic-by-finite groups, amalgamating central cyclic subgroups with trivial intersections, are conjugacy separable.

• East Asian mathematical journal
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• 제33권1호
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• pp.45-52
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• 2017

Motivated by the problem of determining all right ideals of a group algebra FG for a finite group G over a finite field F, we explicitly determine the faithful irreducible representations of some finite metacylic groups over finite fields. By using that result, we determine the structure of all right ideals of the group algebra for the symmetric group $S_3$ over a finite field F, as an example.

• Journal of the Korean Statistical Society
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• 제29권1호
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• pp.29-44
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• 2000

In this paper, we consider one-level rotation designs with finite rotation groups such that the design satisfies two basic requirements: all rotation groups are included in any given survey period, and overlapping rates depend only on the time lag. First we present the necessary number of rotation groups and a rule for the length of time the sample units are to be in or out of the sample to satisfy the requirements. Second, an algorithm is presented to put rotation groups to proper positions in a panel in order to include all finite rotation groups for any survey period. Third, we define an one-level rotation pattern which is invariant in the survey period and has useful properties in practical sense.

• 대한수학회논문집
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• 제11권2호
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• pp.303-310
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• 1996

We define a group property of finite base which is closely related to finite Pr$\ddot{u}$fer rank, and then study the class of groups having such a property.