• 대한수학회지
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• 제56권1호
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• pp.285-287
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• 2019

• 대한수학회지
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• 제32권4호
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.

• 대한수학회논문집
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• 제11권3호
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• pp.575-584
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• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

• 한국수학사학회지
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• 제18권1호
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• pp.75-84
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• 2005

본 논문은 군표현에 관한 역사적 배경을 알아보고, 유한군의 기약지표에 대한 어떤 조건하에서 그 군이 자명하지 않는 아벨 정규부분군을 가짐에 대한 성질들과 기약지표들의 적에 대한 성질을 증명한다.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.353-362
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• 2005

In this paper we prove that if G is a finite group, $^2D_{n}(3)(9{\le}n = 2^m + 1\;not a prime)$, G and M have the same order components, then G$\cong$M.

• 대한수학회보
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• 제48권1호
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• pp.79-83
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• 2011

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.653-659
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• 2009

It is proved that if $M\;=\;B_p(3)$ or $C_p(3)$, p is an odd prime, G is a finite group and has the same order components of M, then $G\;{\cong}\;Bp(3)$ or $C_p(3)$.

• 대한수학회보
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• 제57권6호
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• pp.1475-1479
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• 2020

Let G be a finite group and ${\sigma}_1(G)={\frac{1}{{\mid}G{\mid}}}\;{\sum}_{H{\leq}G}\;{\mid}H{\mid}$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of G, we prove that if ${\sigma}_1(G)<{\frac{117}{20}}$, then G is solvable. This partially solves an open problem posed in [9].

• 대한수학회보
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• 제59권3호
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• pp.781-787
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• 2022

In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra 𝔽_qG can be deduced from a subalgebra 𝔽_q(G/H) of factor group G/H of G, where H is a normal subgroup of G of prime order P. Here, we assume that q = p^r for some prime p and the center of each Wedderburn component of 𝔽_qG is the coefficient field 𝔽_q.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.75-96
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• 2006

Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.