Search results for "table"
showing 10 items of 2807 documents
Saturated formations and products of connected subgroups
2011
Abstract For a non-empty class of groups C , two subgroups A and B of a group G are said to be C -connected if 〈 a , b 〉 ∈ C for all a ∈ A and b ∈ B . Given two sets π and ρ of primes, S π S ρ denotes the class of all finite soluble groups that are extensions of a normal π-subgroup by a ρ-group. It is shown that in a finite group G = A B , with A and B soluble subgroups, then A and B are S π S ρ -connected if and only if O ρ ( B ) centralizes A O π ( G ) / O π ( G ) , O ρ ( A ) centralizes B O π ( G ) / O π ( G ) and G ∈ S π ∪ ρ . Moreover, if in this situation A and B are in S π S ρ , then G is in S π S ρ . This result is then extended to a large family of saturated formations F , the so-c…
BOUNDING THE NUMBER OF IRREDUCIBLE CHARACTER DEGREES OF A FINITE GROUP IN TERMS OF THE LARGEST DEGREE
2013
We conjecture that the number of irreducible character degrees of a finite group is bounded in terms of the number of prime factors (counting multiplicities) of the largest character degree. We prove that this conjecture holds when the largest character degree is prime and when the character degree graph is disconnected.
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.
On the consequences of the standard polynomial
1998
The purpose of this paper is to shed some light on the polynomial identities of low degree for the n × n matrix algebra over a field of characteristic 0.Our main result is that we have found all the consequences of degree n + 2 of the standard polynomial have calculated the S n+2-character of the T-ideal generated by this polynomial.
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.
Periodic Solutions of the Second Order Quadratic Rational Difference Equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}} $$ x n + 1 = α ( 1 + x n ) x n…
2016
The aim of this article is to investigate the periodic nature of solutions of a rational difference equation $$x_{n+1}=\frac{\alpha }{(1+x_n)x_{n-1}}. {(*)} $$ We explore Open Problem 3.3 given in Amleh et al. (Int J Differ Equ 3(1):1–35, 2008, [2]) that requires to determine all periodic solutions of the equation (*). We conclude that for the equation (*) there are no periodic solution with prime period 3 and 4. Period 7 is first period for which exists nonnegative parameter \(\alpha \) and nonnegative initial conditions.
The minimal number of characters over a normal p-subgroup
2007
Abstract If N is a normal p-subgroup of a finite group G and θ ∈ Irr ( N ) is a G-invariant irreducible character of N, then the number | Irr ( G | θ ) | of irreducible characters of G over θ is always greater than or equal to the number k p ′ ( G / N ) of conjugacy classes of G / N consisting of p ′ -elements. In this paper, we investigate when there is equality.
Finite Group Elements where No Irreducible Character Vanishes
1999
AbstractIn this paper, we consider elements x of a finite group G with the property that χ(x)≠0 for all irreducible characters χ of G. If G is solvable and x has odd order, we show that x must lie in the Fitting subgroup F(G).
Real constituents of permutation characters
2022
Abstract We prove a broad generalization of a theorem of W. Burnside about the existence of real characters of finite groups to permutation characters. If G is a finite group, under the necessary hypothesis of O 2 ′ ( G ) = G , we can also give some control on the parity of multiplicities of the constituents of permutation characters (a result that needs the Classification of Finite Simple Groups). Along the way, we give a new characterization of the 2-closed finite groups using odd-order real elements of the group. All this can be seen as a contribution to Brauer's Problem 11 which asks how much information about subgroups of a finite group can be determined by the character table.
Characters and Sylow 2-subgroups of maximal class revisited
2018
Abstract We give two ways to distinguish from the character table of a finite group G if a Sylow 2-subgroup of G has maximal class. We also characterize finite groups with Sylow 3-subgroups of order 3 in terms of their principal 3-block.