• Title/Summary/Keyword: finite group

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ERGODICITY AND RANDOM WALKS ON A COMPACT GROUP

  • CHOE, GEON HO
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.1
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    • pp.25-33
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    • 2001
  • Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

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PROJECTIVE SCHUR ALGEBRAS AS CLASS ALGEBRAS

  • Choi, Eun-Mi;Lee, Hei-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.803-814
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    • 2001
  • A projective Schur algebra associated with a partition of finite group G can be constructed explicitly by defining linear transformations of G. We will consider various linear transformations and count the number of equivalent classes in a finite group. Then we construct projective Schur algebra dimension is determined by the number of classes.

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ON PROJECTIVE REPRESENTATIONS OF A FINITE GROUP AND ITS SUBGROUPS I

  • Park, Seung-Ahn;Park, Eun-Mi
    • Journal of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.387-397
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    • 1996
  • Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

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THE STRUCTURE OF SEMIPERFECT RINGS

  • Han, Jun-Cheol
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.425-433
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    • 2008
  • Let R be a ring with identity $1_R$ and let U(R) denote the group of all units of R. A ring R is called locally finite if every finite subset in it generates a finite semi group multiplicatively. In this paper, some results are obtained as follows: (1) for any semilocal (hence semiperfect) ring R, U(R) is a finite (resp. locally finite) group if and only if R is a finite (resp. locally finite) ring; U(R) is a locally finite group if and only if U$(M_n(R))$ is a locally finite group where $M_n(R)$ is the full matrix ring of $n{\times}n$ matrices over R for any positive integer n; in addition, if $2=1_R+1_R$ is a unit in R, then U(R) is an abelian group if and only if R is a commutative ring; (2) for any semiperfect ring R, if E(R), the set of all idempotents in R, is commuting, then $R/J\cong\oplus_{i=1}^mD_i$ where each $D_i$ is a division ring for some positive integer m and |E(R)|=$2^m$; in addition, if 2=$1_R+1_R$ is a unit in R, then every idempotent is central.

ON DECOMPOSABILITY OF FINITE GROUPS

  • Arhrafi, Ali-Reza
    • 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.

THE NIELSEN THEOREM FOR SEIFERT FIBERED SPACES OVER LOCALLY SYMMETRIC SPACES

  • RAYMOND, FRANK
    • Journal of the Korean Mathematical Society
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    • v.16 no.1
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    • pp.87-93
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    • 1979
  • In this note the geometric realization of a finite group of homotopy classes of self homotopy equivalences by a finite group of diffeomorphisms is investigated. In order for this to be accomplished an algebraic condition, which guarantees a certain group extension exists, must be satisfied. It is shown for a geometrically interesting class of aspherical manifolds, called injective Seifert fiber spaces over a locally symmetric space, that this necessary algebraic condition is also sufficient for geometric realization.

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INDEX AND STABLE RANK OF C*-ALGEBRAS

  • Kim, Sang Og
    • Korean Journal of Mathematics
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    • v.7 no.1
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    • pp.71-77
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    • 1999
  • We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

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