scholarly journals On the Chern classes of the regular representations of some finite groups

1982 ◽  
Vol 25 (3) ◽  
pp. 259-268 ◽  
Author(s):  
Benjamin M. Mann ◽  
R. James Milgram
Keyword(s):  
Finite Groups ◽  
Regular Representation ◽  
Symmetric Groups ◽  
Chern Classes ◽  
Proved Theorem ◽  
Regular Representations ◽  
Modular Invariants ◽  
Representation Rings ◽  
Cobordism Ring ◽  
Primary Torsion

In studying the cohomology of the symmetric groups and its applications in topology one is led to certain questions concerning the representation rings of special subgroups of . In this note we calculate the Chern classes of the regular representation of (Z/p)n where p is a fixed odd prime in terms of certain modular invariants first described by L. E. Dickson in 1911. In a later paper [9] we apply these results to study the odd primary torsion in the PL cobordism ring. Some indications of this application are given in Sections 10–12 where we apply the result above to obtain information about the cohomology of . After circulation of this note in preprint form we learned that H. Mui [10], has also proved Theorem 6.2.

scholarly journals The Plancherel formula for the horocycle space and generalizations

1996 ◽  
Vol 61 (1) ◽  
pp. 42-56 ◽  
Author(s):  
Ronald L. Lipsman
Keyword(s):  
Harmonic Analysis ◽  
Regular Representation ◽  
Plancherel Formula ◽  
Intertwining Operators ◽  
Direct Integral ◽  
Regular Representations ◽  
Spectral Distributions ◽  
Theoretic Technique ◽  
Direct Integral Decomposition ◽  
Integral Decomposition

AbstractThe Plancherel formula for the horocycle space, and several generalizations, is derived within the framework of quasi-regular representations which have monomial spectrum. The proof uses only machinery from the Penney-Fujiwara distribution-theoretic technique; no special semisimple harmonic analysis is needed. The Plancherel formulas obtained include the spectral distributions and the intertwining operators that effect the direct integral decomposition of the quasi-regular representation.

The Use of S-Functions in Combinatorial Analysis

1968 ◽  
Vol 20 ◽  
pp. 808-841 ◽  
Author(s):  
Ronald C. Read
Keyword(s):  
Graph Theory ◽  
Finite Groups ◽  
Symmetric Functions ◽  
Symmetric Groups ◽  
Combinatorial Problems ◽  
Combinatorial Analysis

The aim of this paper is to present a unified treatment of certain theorems in Combinatorial Analysis (particularly in enumerative graph theory), and their relations to various results concerning symmetric functions and the characters of the symmetric groups. In particular, it treats of the simplification that is achieved by working with S-functions in preference to other symmetric functions when dealing with combinatorial problems. In this way it helps to draw closer together the two subjects of Combinatorial Analysis and the theory of Finite Groups. The paper is mainly expository; it contains little that is really new, though it displays several old results in a new setting.

Graphical Regular Representations of Non-Abelian Groups, II

1972 ◽  
Vol 24 (6) ◽  
pp. 1009-1018 ◽  
Author(s):  
Lewis A. Nowitz ◽  
Mark E. Watkins
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Regular Representation ◽  
Affirmative Answer ◽  
Roman Numeral ◽  
Regular Representations ◽  
Graphical Regular Representation ◽  
Bold Face

The present paper is a sequel to the previous paper bearing the same title by the same authors [3] and which will be hereafter designated by the bold-face Roman numeral I. Further results are obtained in determining whether a given finite non-abelian group G has a graphical regular representation. In particular, an affirmative answer will be given if (|G|, 6) = 1.Inasmuch as much of the machinery of I will be required in the proofs to be presented and a perusal of I is strongly recommended to set the stage and provide motivation for this paper, an independent and redundant introduction will be omitted in the interest of economy.

Suatu Hubungan Kumpulan Pusat–2 dengan Teori Kebarangkalian

2012 ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Hasimah Sapiri
Keyword(s):  
Probability Theory ◽  
Finite Group ◽  
Finite Groups ◽  
Random Element ◽  
Symmetric Groups ◽  
Finite Rings ◽  
Nonabelian Group ◽  
Central Group ◽  
Upper Limit

Penentuan darjah keabelanan bagi suatu kumpulan tak abelan telah diperkenalkan untuk kumpulan simetri oleh Erdos dan Turan [1]. Dalam tahun 1973, Gustafson [2] mengkajinya bagi kumpulan terhingga sementara MacHale [3] mengkajinya bagi gelanggang terhingga dalam tahun 1976. Dalam kajian ini, beberapa keputusan yang berkaitan dengan Pn(G), kebarangkalian bahawa suatu unsur rawak dengan kuasa ke–n dalam suatu kumpulan pusat–2 G adalah kalis tukar tertib dengan unsur rawak yang lain dalam kumpulan yang sama, akan diberikan. Seterusnya, batas atas bagi P2(G) diperoleh. Kata kunci: Teori kebarangkalian, teori kumpulan, kumpulan terhingga, kalis tukar tertib The determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos & Turan [1]. In 1973, Gustafson [2] did this research for the finite groups while MacHale [3] determined the abelianness for finite rings in 1976. In this research, some results on Pn(G), the probability that the n–th power of a random element in a 2–central group G commutes with another random element from the same group, will be presented. Furthermore, the upper limit of P2(G) is obtained. Key words: Probability theory, group theory, finite group, commutative

scholarly journals Chief Series and Right Regular Representations of Finite p-Groups

1988 ◽  
Vol 44 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Felix Leinen
Keyword(s):  
Regular Representation ◽  
Locally Finite ◽  
Regular Representations ◽  
Direct Limits ◽  
One To One ◽  
The Right

AbstractWe study the embeddings of a finite p-group U into Sylow p-subgroups of Sym (U) induced by the right regular representation p: U→ Sym(U). It turns out that there is a one-to-one correspondence between the chief series in U and the Sylow p-subgroups of Sym (U) containing Up. Here, the Sylow p-subgroup Pσ of Sym (U) correspoding to the chief series σ in U is characterized by the property that the intersections of Up with the terms of any chief series in Pσ form σp. Moreover, we see that p: U→ Pσ are precisely the kinds of embeddings used in a previous paper to construct the non-trivial countable algebraically closed locally finite p-groups as direct limits of finite p-groups.

Strong Gelfand pairs of symmetric groups

2020 ◽  
pp. 2150054
Author(s):  
Gradin Anderson ◽  
Stephen P. Humphries ◽  
Nathan Nicholson
Keyword(s):  
Commutative Ring ◽  
Finite Groups ◽  
Symmetric Groups ◽  
Maximal Dimension ◽  
Gelfand Pair ◽  
Gelfand Pairs ◽  
Schur Ring

A strong Gelfand pair is a pair [Formula: see text], of finite groups such that the Schur ring determined by the [Formula: see text]-classes [Formula: see text], is a commutative ring. We find all strong Gelfand pairs [Formula: see text]. We also define an extra strong Gelfand pair [Formula: see text], this being a strong Gelfand pair of maximal dimension, and show that in this case [Formula: see text] must be abelian.

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