Search results for "Number"

Hyper-abelian groups with finite co-central rank

2004

AbstractA group G has finite co-central rank s if there exists a least non-negative integer s such that every finitely generated subgroup H can be generated by at most s elements modulo the centre of H. The investigation of such groups has been started in [J.P. Sysak, A. Tresch, J. Group Theory 4 (2001) 325]. It is proved that hyper-abelian groups with finite co-central rank are locally soluble. The interplay between the Prüfer rank condition, the condition of having finite abelian section rank and the finite co-central rank condition is studied. As one result, a hyper-abelian group G with finite co-central rank has an ascending series with abelian factors of finite rank and every chief fac…

Automorphisms of the integral group rings of some wreath products

1991

Miglioramento dell'approssimazione delle radici complesse, semplici e multiple di equazioni algebriche a coefficienti reali

1968

The paper shows an iterative procedure by which, starting from an approximate value of a root,z0=x0+jy0, of an algebraic equationF(z)=0, a sequence of values {zn} is obtained, aproximating the corresponding exact root; under certain conditions.

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.

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.

Fittingmengen und lockettabschnitte

1990

Abstract The theory of Lockett sections is transferred from Fitting classes to Fitting sets. This in general works only partially; in some special groups (which I call “mobility” groups), however, among these the stable linear groups, a literal translation of the Fitting class theory is possible. As the groups relevant in outer Fitting pairs actually are mobility groups, a new way of deriving information on the Lockett section of a Fitting class arises. This is used to present a simplified, if nonsoluble, counter-example to Lockett's conjecture and to decide a related question. Also, an approach to generating Fitting classes is given.

Two Questions of L. A. Shemetkov on Critical Groups

1996

Throughout the paper we consider only finite groups. Let X be a class of groups. A group G is called s-critical for X , or simply X-critical, if G is not in X but all proper subgroups of G are in X. w Ž .x Ž . Following Doerk and Hawkes 3, VII, 6.1 , we denote Crit X the class s of all X-critical groups. Knowledge of the structure of the groups in Ž . Crit X for a class of groups X can often help one to obtain detailed s information for the structure of the groups belonging to X. Ž w Ž .x. O. J. Schmidt see 5, III, 5.2 studied the N-critical groups, where N is the formation of the nilpotent groups. These groups are also called w x Schmidt groups. In 2 , answering to a question posed by Shem…

Co-learnability and FIN-identifiability of enumerable classes of total recursive functions

1994

Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. number…

On the spectrum of linear combinations of two projections inC*-algebras

2010

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.