• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.227-232
• /
• 2006

We study some dynamical properties in the context of bitransformation groups, and show that if (H,X,T) is a bitransformation group such that (H,X) is almost periodic and (X/H,T) is pointwise almost periodic $T_2$ and $x{\in}X$, then $E_x=\{q{\in}E(H,X){\mid}qx{\in}{\overline{xT}\}$ is a compact $T_2$ topological group and $E_{qx}=E_x(q{\in}E(H,X))$ when H is abelian, where E(H,X) is the enveloping semigroup of the transformation group (H,X).

• 충청수학회지
• /
• 제23권4호
• /
• pp.749-755
• /
• 2010

We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.

• 대한수학회지
• /
• 제54권1호
• /
• pp.177-191
• /
• 2017

In this note we consider the right unit-duo ring property on the powers of elements, and introduce the concept of weakly right unit-duo ring. We investigate first the properties of weakly right unit-duo rings which are useful to the study of related studies. We observe next various kinds of relations and examples of weakly right unit-duo rings which do roles in ring theory.

• 한국수학사학회지
• /
• 제18권1호
• /
• pp.75-84
• /
• 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.

• 대한수학회지
• /
• 제50권6호
• /
• pp.1213-1222
• /
• 2013

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field $\mathbb{K}$ where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that char $\mathbb{K}$ does not divide |G| but there is no assumption made of $\mathbb{K}$ being algebraically closed.

• 충청수학회지
• /
• 제10권1호
• /
• pp.161-175
• /
• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• 대한수학회지
• /
• 제53권2호
• /
• pp.263-286
• /
• 2016

We discuss relations between Galois coverings of compact Riemann surfaces and their Jacobi varieties. We prove a theorem of a kind of Galois correspondence for Abelian subvarieties of Jacobi varieties. We also prove a theorem on the sets of points in Jacobi varieties fixed by Galois group actions.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.53-59
• /
• 2016

Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.

• 대한수학회보
• /
• 제33권3호
• /
• pp.481-485
• /
• 1996

Let G be an abelian topological group and $x_{ij} \in G$ for all $i, j \in N$ such that the series $\sum_{j=i}^{\infty} x_{ij}$ is subseries convergent for each i.

• 대한수학회논문집
• /
• 제11권2호
• /
• pp.311-314
• /
• 1996

Let G be an abelian group of finite rink and E be the endomorphism ring of G. Then G is a left E-module by defining $f\cdota = f(a)$ for $f \in E$ and $a \in G$. In this case a condition for an E-module G to be regular is given.