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SPLITTINGS FOR THE BRAID-PERMUTATION GROUP
Jeong, Chan-Seok,Song, Yong-Jin Korean Mathematical Society 2003 대한수학회지 Vol.40 No.2
The braid-permutation group is a group of welded braids which is the extension of Artin's braid groups by the symmetric groups. It is also described as a subgroup of the automorphism group of a free group. We also show that the plus-construction of the classifying space of the infinite braid-permutation group has the following two types of splittings BBP(equation omitted) B∑(equation omitted) $\times$ X, BBP(equation omitted) B $^{+}$$\times$ Y=S$^1$$\times$Y, where X, Y are some spaces.
MULTIPLICITY-FREE ACTIONS OF THE ALTERNATING GROUPS
Balmaceda, Jose Maria P. Korean Mathematical Society 1997 대한수학회지 Vol.34 No.2
A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.
ON A PERMUTABLITY PROBLEM FOR GROUPS
TAERI, BIJAN 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
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.
GROUP OF POLYNOMIAL PERMUTATIONS OF Zpr
이관규,이혜숙 호남수학회 2012 호남수학학술지 Vol.34 No.4
The set of all polynomial permutations of Zpr forms a group. We investigate the structure of the group and some related groups, and completely determine the structure of the group of all polynomial permutations of Zp2 .
GROUP OF POLYNOMIAL PERMUTATIONS OF ℤ<sub>p</sub><sub>r</sub>
Lee, Kwankyu,Lee, Heisook The Honam Mathematical Society 2012 호남수학학술지 Vol.34 No.4
The set of all polynomial permutations of $\mathbb{Z}_{p^r}$ forms a group. We investigate the structure of the group and some related groups, and completely determine the structure of the group of all polynomial permutations of $\mathbb{Z}_{p^2}$.
SUBPERMUTABLE SUBGROUPS OF SKEW LINEAR GROUPS AND UNIT GROUPS OF REAL GROUP ALGEBRAS
Le, Qui Danh,Nguyen, Trung Nghia,Nguyen, Kim Ngoc Korean Mathematical Society 2021 대한수학회보 Vol.58 No.1
Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ 3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.
Multivariate Nonparametric Tests for Grouped and Right Censored Data
Park Hyo-Il,Na Jong-Hwa,Hong Seungman The Korean Reliability Society 2005 International Journal of Reliability and Applicati Vol.6 No.1
In this paper, we propose a nonparametric test procedure for the multivariate, grouped and right censored data for two sample problem. For the construction of the test statistic, we use the linear rank statistics for each component and apply the permutation principle for obtaining the null distribution. For the large sample case, the asymptotic distribution is derived under the null hypothesis with the additional assumption that two censoring distributions are also equal. Finally, we illustrate our procedure with an example and discuss some concluding remarks. In appendices, we derive the expression of the covariance matrix and prove the asymptotic distribution.
Nonparametric Tests for Grouped K-Sample Problem
Park, Hyo-Il The Korean Statistical Society 2006 Communications for statistical applications and me Vol.13 No.2
We propose a nonparametric test procedure for the K-sample problem with grouped data. We construct the test statistics using the scores derived for the linear model based on likelihood ratio principle and obtain asymptotic distribution. Also we illustrate our procedure with an example. Finally we discuss some concluding remarks.
Permutable and Mutually Permutable Fuzzy Bigroup
Akinola L.S,Agboola A.A.A. 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.3
In this paper, we introduce the concept of restricted fuzzy bigroup which is an improvement on the existing concept of fuzzy bigroup. We also extend the idea of permutability and mutually permutability to the rede¯ned fuzzy bigroup. We de¯ne permutable and mutually permutable fuzzy bigroup of a bigroup and study some of their properties.