Radicals of semi-group rings
Radicals of symmetric cellular algebras
For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.
Random Cayley graphs are expanders: a simple proof of the Alon-Roichman theorem.
Rational Functions Invariant under a Finite Abelian Group.
Rational Representations of Finite Groups and Their Euler Class.
Realisierbarkeit von Darstellungen endlicher Gruppen in Einheitswurzelkörpern.
Realizing maps between modules over Tate cohomology rings.
Recent results on the derived length of Lie solvable group algebras.
Recognition of characteristically simple group by character degree graph and order
The character degree graph of a finite group is the graph whose vertices are the prime divisors of the irreducible character degrees of and two vertices and are joined by an edge if divides some irreducible character degree of . It is proved that some simple groups are uniquely determined by their orders and their character degree graphs. But since the character degree graphs of the characteristically simple groups are complete, there are very narrow class of characteristically simple...
Recognition of some families of finite simple groups by order and set of orders of vanishing elements
Let be a finite group. An element is called a vanishing element if there exists an irreducible complex character of such that . Denote by the set of orders of vanishing elements of . Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let be a finite group and a finite nonabelian simple group such that and . Then . We answer in affirmative this conjecture for , where and either , or is a prime number, and , where and either...
Reduced unstable -modules and the modular representation theory of the symmetric groups
Regular character tables of symmetric groups.
Regular Orbits fo Hall ...-subgroups.
Regularisation and the Mullineux map.
Relation modules of finite groups and related topics.
Relation modules of infinite groups, II
Let F n denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ F m ↠ G and S ↪ F m ↠ G are presentations of G and let and denote the associated relation modules of G. It is well known that even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G that has presentations...
Relative cyclic homology and the Bass conjecture.
Relative Relation Modules as Generators for Integral Group Rings of Finite Groups.
Relèvement de Brauer et représentations paraboliques de
Remarks on Characters of Discrete Nilpotent Groups.