Search results for "permutation"

A class of imprimitive groups

2010

We classify imprimitive groups inducing the alternating group A4 on the set of blocks, with the inertia subgroup satisfying some very natural geometrical conditions which force the group to operate linearly.

Homomorphs and wreath product extensions

1982

A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .

Some contributions to the theory of transformation monoids

2019

The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J…

Permutation properties and the fibonacci semigroup

1989

Cyclic and lift closures for k…21-avoiding permutations

2011

We prove that the cyclic closure of the permutation class avoiding the pattern k(k-1)...21 is finitely based. The minimal length of a minimal permutation is 2k-1 and these basis permutations are enumerated by (2k-1).c"k where c"k is the kth Catalan number. We also define lift operations and give similar results. Finally, we consider the toric closure of a class and we propose some open problems.

HEIGHTS OF CHARACTERS IN BLOCKS OF $p$-SOLVABLE GROUPS

2005

In this paper, it is proved that if $B$ is a Brauer $p$ -block of a $p$ -solvable group, for some odd prime $p$ , then the height of any ordinary character in $B$ is at most $2b$ , where $p^b$ is the largest degree of the irreducible characters of the defect group of $B$ . Some other results that relate the heights of characters with properties of the defect group are obtained.

Quantum Queries on Permutations with a Promise

2009

This paper studies quantum query complexities for deciding (exactly or with probability 1.0) the parity of permutations of n numbers, 0 through n *** 1. Our results show quantum mechanism is quite strong for this non-Boolean problem as it is for several Boolean problems: (i) For n = 3, we need a single query in the quantum case whereas we obviously need two queries deterministically. (ii) For even n , n /2 quantum queries are sufficient whereas we need n *** 1 queries deterministically. (iii) Our third result is for the problem deciding whether the given permutation is the identical one. For this problem, we show that there is a nontrivial promise such that if we impose that promise to the …

Central Units, Class Sums and Characters of the Symmetric Group

2010

In the search for central units of a group algebra, we look at the class sums of the group algebra of the symmetric group S n in characteristic zero, and we show that they are units in very special instances.

Group algebras whose units satisfy a group identity

1997

Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.

The complex of words and Nakaoka stability

2005

We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…