Schur indices of perfect groups

It has been noticed by many authors that the Schur indices of the irreducible characters of many quasi-simple finite groups are at most . A conjecture has emerged that the Schur indices of all irreducible characters of all quasi-simple finite groups are at most . We prove that this conjecture cannot be extended to the set of all finite perfect groups. Indeed, we prove that, given any positive integer , there exist irreducible characters of finite perfect groups of chief length which have Schur index .

     

Schur indices and abelian defect groups

We show that the irreducible characters lying in 2-blocks of finite solvable groups with abelian defect groups have trivial 2-local Schur indices.     

Finite groups with its power automorphism groups having small indices

In this paper, a finite group G with IAut（G） ： P（G）I ~- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies ｜Aut（G） ： P（G）｜= pq if and only if Aut（G）/P（G） ≌S3. Also, some other classes of finite groups are investigated and classified, which are necessary for the proof of our main results.     

Use of individual and group seasonal indices in subaggregate demand forecasting

An individual seasonal indices (ISI) method and two group seasonal indices (GSI) methods proposed in the literature are compared, based on two models. Rules have been established to choose between these methods and insights are gained on the conditions under which one method outperforms the others. Simulation findings confirm that using the rules improves forecasting accuracy against universal application of these methods.     

Formation of segregated and integrated groups

A model of group formation is presented such that the number of groups is fixed, and a person can only join a group if the group’s members approve the person’s joining. Agents have either local status preferences (each agent wants to be the highest status agent in his group) or global status preferences (each agent wants to join the highest status group that she can join). For both preference types, conditions are provided which guarantee the existence of a segregated stable partition such that similar people are grouped together, and conditions are provided which guarantee the existence of an integrated stable partition such that dissimilar people are grouped together. Additionally, in a dynamic framework we show that if a new empty group is added to a segregated stable partition, then integration may occur.     

Schur indices of characters of groups related to finite sporadic simple groups

LetG be a finite sporadic simple group. Then there exist groupsn.G., n.G.2 and, in casen is even,n.G.2i, the group isoclinic to but not isomorphic ton.G.2. The Schur indices of all irreducible characters of these groups are computed. In a previous paper this was done for the groupsn.G (with one exception). The division algebra corresponding to a character is determined by all the local Schur indices. These are all listed in the tables in Section 6 using the notation from the ATLAS.     

On finite groups with some subgroups of prime indices

We establish the solvability of each finite group whose every proper nonmaximal subgroup lies in some subgroup of prime index.     

Descents, inversions, and major indices in permutation groups

A multivariate generating function involving the descent, major index, and inversion statistic first given by Ira Gessel is generalized to other permutation groups. We provide generating functions for variants of these three statistics for the Weyl groups of type B and D, wreath product groups, and multiples of permutations. All of our ideas are combinatorial in nature and exploit fundamental relationships between the elementary and homogeneous symmetric functions.     

On the normal indices of proper subgroups of finite groups

We extended the normal index from maximal subgroups to proper subgroups. We give a quantitative version of all results obtained by using c-normal subgroups and obtain some new characterizations of solvable, supersolvable and nilpotent groups by the normal indices of proper subgroups.     

A characterization of the finite simple groups with set of indices of their maximal subgroups

We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups.     

Structure of unitary groups over finite group rings and its application

In this paper, we determine all the normal forms of Hermitian matrices over finite group rings R = F_q²GR = {F_{{q^2}}}G, where q = p ^α , G is a commutative p-group with order p ^β . Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over R through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters.     

Finite groups in which the normalizers of pairwise intersections of Sylow 2-subgroups have odd indices

All finite semisimple groups are described in which the normalizers of pairwise intersections of Sylow 2-subgroups have odd indices; thereby, Problem 5.14(v) from the Kourovka Notebook is solved in the main.     

Multiplier completion of Banach algebras with application to quantum groups

Archiv der Mathematik - Let $${{mathcal {A}}}$$ be a Banach algebra and let $$varphi $$ be a non-zero character on $${{mathcal {A}}}$$ . Suppose that $${{mathcal {A}}}_M$$ is the closure of the...