Search results for "Number"
showing 10 items of 3939 documents
Soluble groups with their centralizer factor groups of bounded rank
2007
Abstract For a group class X , a group G is said to be a C X -group if the factor group G / C G ( g G ) ∈ X for all g ∈ G , where C G ( g G ) is the centralizer in G of the normal closure of g in G . For the class F f of groups of finite order less than or equal to f , a classical result of B.H. Neumann [Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951) 178–187] states that if G ∈ C F f , the commutator group G ′ belongs to F f ′ for some f ′ depending only on f . We prove that a similar result holds for the class S r ( d ) , the class of soluble groups of derived length at most d which have Prufer rank at most r . Namely, if G ∈ C S r ( d ) , then G ′ ∈ S d…
A variation on theorems of Jordan and Gluck
2006
Abstract Gluck proved that any finite group G has an abelian subgroup A such that | G : A | is bounded by a polynomial function of the largest degree of the complex irreducible characters of G . This improved on a previous bound of Isaacs and Passman. In this paper, we present a variation of this result that looks at the number of prime factors. All these results, in turn, may be seen as variations on the classical theorem of Jordan on linear groups.
Zu einem Satz von Isaacs �ber das Casus-Irreducibilis Ph�nomen
2000
Let \(\Omega \) be a field (of characteristic 0). A prime p is called “bose” (naughty) if \(\Omega \) contains all p-th roots of unity. In this paper the theorem is proved: Let K be an admissible subfield of \(\Omega \) (i.e. for each prime p K contains all p-th roots of unity lying in \(\Omega \)), a an algebraic element of \(\Omega /K\) which is contained in a repeated radical extension of K lying in \(\Omega \). Furthermore let the normal hull L of a over K be contained in \(\Omega \). Then all prime divisors of \(\mid L : K \mid \) are naughty (and L is a repeated radical extension of K with naughty prime exponents). This result generalises a theorem of Isaacs [1] who treats the case \(…
Varieties with at most quadratic growth
2010
Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions cn(V); n = 1; 2, … and here we study varieties of polynomial growth. Recently, for any real number a, 3 < a < 4, a variety V was constructed satisfying C1n^a < cn(V) < C2n^a; for some constants C1;C2. Motivated by this result here we try to classify all possible growth of varieties V such that cn(V) < Cn^a; with 0 < a < 2, for some constant C. We prove that if 0 < a < 1 then, for n large, cn(V) ≤ 1, whereas if V is a commutative variety and 1 < a < 2, then lim logn cn(V) = 1 o…
Central idempotents and units in rational group algebras of alternating groups
1998
Let ℚAn be the group algebra of the alternating group over the rationals. By exploiting the theory of Young tableaux, we give an explicit description of the minimal central idempotents of ℚAn. As an application we construct finitely many generators for a subgroup of finite index in the centre of the group of units of ℚAn.
K-theory of function rings
1990
AbstractThe ring R of continuous functions on a compact topological space Xwith values in R or C is considered. It is shown that the algebraic K-theory of such rings with coefficients in ZkZ, k any positive integer, agrees with the topological K-theory of the underlying space X with the same coefficient rings. The proof is based on the result that the map from Rδ (R with discrete topology) to R (R with compact-open topology) induces a natural isomorphism between the homologies with coefficients in ZkZ of the classifying spaces of the respective infinite general linear groups. Some remarks on the situation with X not compact are added.
Y-proper graded cocharacters of upper triangular matrices of order m graded by the m-tuple ϕ=(0,0,1,…,m−2)
2015
Abstract Let F be a field of characteristic 0. We consider the algebra UT m ( F ) of upper triangular matrices of order m endowed with an elementary Z m -grading induced by the m-tuple ϕ = ( 0 , 0 , 1 , … , m − 2 ) , then we compute its Y-proper graded cocharacter sequence and we give the explicit formulas for the multiplicities in the case m = 2 , 3 , 4 , 5 .
Type and Cotype in Vector-Valued Nakano Sequence Spaces
2001
AbstractGiven a sequence of Banach spaces {Xn}n and a sequence of real numbers {pn}n in [1,∞), the vector-valued Nakano sequence spaces ℓ({pn},{Xn}) consist of elements {xn}n in ∏nXn for which there is a constant λ>0 such that ∑n(‖xn‖/λ)pn<∞. In this paper we find the conditions on the Banach spaces Xn and on the sequence {pn}n for the spaces ℓ({pn},{Xn}) to have cotype q or type p.
CHARACTERS INDUCED FROM FULLY RAMIFIED SUBGROUPS
2001
Suppose that G is a finite π-separable group, let cf(G) be the space of complex class functions of G and let Irr(G) be the set of the irreducible complex characters of G. Let K be an arbitrary Hall...
On periodic radical groups in which permutability is a transitive relation
2007
Abstract A group G is said to be a PT - group if permutability is a transitive relation in the set of all subgroups of G . Our purpose in this paper is to study PT -groups in the class of periodic radical groups satisfying min- p for all primes p .