Search results for "Conjugacy class"

A note on the support of block idempotents

1994

p-Length andp′-Degree Irreducible Characters Having Values in ℚp

2013

Let G be a p-solvable group of p-length l, where p is any prime. We show that G has at least 2 l irreducible characters of degree coprime to p and having values inside ℚ p . This generalizes a previous result for p = 2 [6] to arbitrary primes. With the same notation, we prove that if p is odd then G has at least 2 l Galois orbits of conjugacy classes of p-elements having values in ℚ p .

On a graph related to permutability in finite groups

2010

For a finite group G we define the graph $\Gamma(G)$ to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes $\{\mathcal {A}, \mathcal {B}\}$ are joined by an edge if for some $\{A \in \mathcal {A},\, B \in \mathcal {B}\, A\}$ and B permute. We characterise those groups G for which $\Gamma(G)$ is complete.

Intersection subgroups of complex hyperplane arrangements

2000

Abstract Let A be a central arrangement of hyperplanes in C n , let M( A ) be the complement of A , and let L ( A ) be the intersection lattice of A . For X in L ( A ) we set A X ={H∈ A : H⫆X} , and A /X={H/X: H∈ A X } , and A X ={H∩X: H∈ A \ A X } . We exhibit natural embeddings of M( A X ) in M( A ) that give rise to monomorphisms from π 1 (M( A X )) to π 1 (M( A )) . We call the images of these monomorphisms intersection subgroups of type X and prove that they form a conjugacy class of subgroups of π 1 (M( A )) . Recall that X in L ( A ) is modular if X+Y is an element of L ( A ) for all Y in L ( A ) . We call X in L ( A ) supersolvable if there exists a chain 0⫅X 1 ⫅⋯⫅X d =X in L ( A ) …

ℏ-Normalizers and local definitions of saturated formations of finite groups

1989

We define, in each finite groupG, h-normalizers associated with a Schunck class ℏ of the formEΦ f with f a formation. We use these normalizers in order to give some sufficient conditions for a saturated formation of finite groups to have a maximal local definition.

An extension of the Burrows-Wheeler Transform and applications to sequence comparison and data compression

2005

We introduce a generalization of the Burrows-Wheeler Transform (BWT) that can be applied to a multiset of words. The extended transformation, denoted by E, is reversible, but, differently from BWT, it is also surjective. The E transformation allows to give a definition of distance between two sequences, that we apply here to the problem of the whole mitochondrial genome phylogeny. Moreover we give some consideration about compressing a set of words by using the E transformation as preprocessing.

An extension of the Burrows-Wheeler Transform

2007

AbstractWe describe and highlight a generalization of the Burrows–Wheeler Transform (bwt) to a multiset of words. The extended transformation, denoted by ebwt, is reversible. Moreover, it allows to define a bijection between the words over a finite alphabet A and the finite multisets of conjugacy classes of primitive words in A∗. Besides its mathematical interest, the extended transform can be useful for applications in the context of string processing. In the last part of this paper we illustrate one such application, providing a similarity measure between sequences based on ebwt.

Groups whose prime graph on conjugacy class sizes has few complete vertices

2012

Abstract Let G be a finite group, and let Γ ( G ) denote the prime graph built on the set of conjugacy class sizes of G. In this paper, we consider the situation when Γ ( G ) has “few complete vertices”, and our aim is to investigate the influence of this property on the group structure of G. More precisely, assuming that there exists at most one vertex of Γ ( G ) that is adjacent to all the other vertices, we show that G is solvable with Fitting height at most 3 (the bound being the best possible). Moreover, if Γ ( G ) has no complete vertices, then G is a semidirect product of two abelian groups having coprime orders. Finally, we completely characterize the case when Γ ( G ) is a regular …

Large subgroups of a finite group of even order

2011

It is shown that if G G is a group of even order with trivial center such that | G | > 2 | C G ( t ) | 3 |G|>2|C_{G}(t)|^{3} for some involution t ∈ G t\in G , then there exists a proper subgroup H H of G G such that | G | > | H | 2 |G|> |H|^{2} . If | G | > | C G ( t ) | 3 |G|>|C_{G}(t)|^{3} and k ( G ) k(G) is the class number of G G , then | G | ≤ k ( G ) 3 |G|\leq k(G)^{3} .

Cyclic Complexity of Words

2014

We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming letters, $x$ and $y$ have the same set of factors. In particular, $y$ is also Sturmian of slope equ…