• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.547-555
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• 1996

In this paper, we shall study the generalized covering group which plays a role for Schur multiplier. We discuss the lifting property over covering group and product of covering groups.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-167
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• 2007

If k is a subfield of $\mathbb{Q}(\varepsilon_m)$ then the cohomology group $H^2(k(\varepsilon_n)/k)$ is isomorphic to $H^2(k(\varepsilon_{n'})/k)$ with gcd(m, n') = 1. This enables us to reduce a cyclotomic k-algebra over $k(\varepsilon_n)$ to the one over $k(\varepsilon_{n'})$. A radical extension in projective Schur algebra theory is regarded as an analog of cyclotomic extension in Schur algebra theory. We will study a reduction of cohomology group of radical extension and show that a Galois cohomology group of a radical extension is isomorphic to that of a certain subextension of radical extension. We then draw a cohomological characterization of radical group.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.265-275
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• 1992

The characteristic free representation theory of the general linear group has found a wide range of applications, ranging from the theory of free resolutions to the symmetric function theory. Representation theory is used to facilitate the calculation of explicit free resolutions of large classes of ideals (and modules). Recently, K. Akin and D. A. Buchsbaum [2] realized the Jacobi-Trudi identity for a Schur function as a resolution of GL$_{n}$-modules. Over a field of characteristic zero, it was observed by A. Lascoux [6]. T.Jozefiak and J.Weyman [5] used the Koszul complex to realize a formula of D.E. Littlewood as a resolution of schur modules. This leads us to further study resolutions of Schur modules of a particular form. In this article we will describe some new classes of finite free resolutions associated to the Pieri type skew Young diagrams. As a special case of these finite free resolutions we obtain the generalized Koszul complex constructed in [1]. In section 2 we review some of the basic difinitions and properties of Schur modules that we shall use. In section 3 we describe certain exact complexes associated to the Pieri type skew partitions. Throughout this article, unless otherwise specified, R is a commutative ring with an identity element and a mudule F is a finitely generated free R-module.e.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.855-865
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• 2012

Recently, we have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x{\wedge}y=1_{G{\wedge}G}$ in the exterior square $G{\wedge}G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m{\wedge}k$ of $H{\wedge}K$ such that $h^m{\wedge}k=1_{H{\wedge}K}$, where $m{\geq}1$ and $H$ and $K$ are arbitrary subgroups of $G$.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.465-471
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• 1998

The class of finite solube groups with zero deficiency known to have soluble lenght five or six is small. In this paper we exhibit some classes of such goups.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.43-49
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• 1979

G를 유한군으로, C를 모든 복소수체로 가정하고, V를 C상에서의 유한차원 벡터공간이라 하자. V상에서의 G의 사영적 표시는, X, $y{\epsilon}G$이고 ${\alpha}:\;G{\times}G{\rightarrow}C$를 Facto set이라 할 때 $T(x)T(y)=T(xy){\alpha}(x,y)$이 되는 함수 $T=\;G{\rightarrow}GL(V)$를 말한다. 본 논문의 목적은 군에 대한 Extension theory를 사용해서, G상의 factor set들의 동치류들은 G의 Second Cohomology group과 동형이라는 것을 증명하는 것이다.