Search results for "Group Theory"
showing 10 items of 703 documents
Induction and Character Correspondences in Groups of Odd Order
2002
Abstract Let P be a Sylow p -subgroup of G . By Irr p ′ ( G ), we denote the set of irreducible characters of G which have degree not divisible by p . When G is a solvable group of odd order, M. Isaacs constructed a natural one-to-one correspondence *:Irr p ′ ( G ) → Irr p ′ ( N G ( P )) which depends only on G and P . In this paper, we show that if ξ G = χ ∈ Irr p ′ ( G ), then (ξ*) N G ( P ) = χ*.
Groups with a small average number of zeros in the character table
2021
Abstract We classify finite groups with a small average number of zeros in the character table.
ZEROS OF CHARACTERS ON PRIME ORDER ELEMENTS
2001
Suppose that G is a finite group, let χ be a faithful irreducible character of degree a power of p and let P be a Sylow p-subgroup of G. If χ(x) ≠ 0 for all elements of G of order p, then P is cyclic or generalized quaternion. * The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country UPV 127.310-EB160/98. † The second author is supported by DGICYT.
Balance Properties and Distribution of Squares in Circular Words
2008
We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalised to non periodic infinite words as well.
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.
The Jordan-Hölder theorem and prefrattini subgroups of finite groups
1995
by A. BALLESTER-BOLINCHES and L. M. EZQUERRO(Received 26 January, 1994)Introduction. All groups considered are finite. In recent years a number ofgeneralizations of the classic Jordan-Holder Theorem have been obtained (see [7],Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but eventheir property of being Frattini or non-Frattini chief factors. In [2] and [13] a newdirection of generalization is presented: the above correspondence can be defined in sucha way that the corresponding non-Frattini chief factors have the same complement(supplement).In this paper we present a necessary a…
Homogeneous products of characters
2004
I. M. Isaacs has conjectured (see \cite{isa00}) that if the product of two faithful irreducible characters of a solvable group is irreducible, then the group is cyclic. In this paper we prove a special case of the following conjecture, which generalizes Isaacs conjecture. Suppose that $G$ is solvable and that $\psi,\phi\in\Irr(G)$ are faithful. If $\psi \phi=m\chi$ where $m$ is a positive integer and $\chi \in \Irr(G)$ then $\psi$ and $\phi$ vanish on $G- Z(G)$. In particular we prove that the above conjecture holds for $p$-groups.
Parabolic Subgroups of Artin Groups
1997
Abstract Let ( A , Σ) be an Artin system. For X ⊆ Σ, we denote by A X the subgroup of A generated by X . Such a group is called a parabolic subgroup of A . We reprove Van der Lek's theorem: “a parabolic subgroup of an Artin group is an Artin group.” We give an algorithm which decides whether two parabolic subgroups of an Artin group are conjugate. Let A be a finite type Artin group, and let A X be a parabolic subgroup with connected associated Coxeter graph. The quasi-centralizer of A X in A is the set of β in A such that β X β −1 = X . We prove that the commensurator of A X in A is equal to the normalizer of A X in A , and that this group is generated by A X and the quasi-centralizer of…
Centralizers of Parabolic Subgroups of Artin Groups of TypeAl,Bl, andDl
1997
Abstract Let ( A , Σ) be an Artin system of one of the types A l , B l , D l . For X ⊆ Σ, we denote by A X the subgroup of A generated by X . Such a group is called a parabolic subgroup of ( A , Σ). Let A X be a parabolic subgroup with connected associated Coxeter graph. We exhibit a generating set of the centralizer of A X in A . Moreover, we prove that there exists X ′ ⊆ Σ such that A X ′ is conjugate to A X and such that the centralizer of A X ′ in A is generated by the centers of all the parabolic subgroups containing A X ′ .
Injectors and Radicals in Products of Totally Permutable Groups
2003
Abstract Two subgroups H and K of a group G are said to be totally permutable if every subgroup of H permutes with every subgroup of K. In this paper the behaviour of radicals and injectors associated to Fitting classes in a product of pairwise totally permutable finite groups is studied.