The partition problem for equifacetal simplices.
The periodic groups saturated by finitely many finite simple groups.
The periodicity conjecture for blocks of group algebras
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
The permutation group induced on a moiety.
The permutation group method for the dilogarithm
We give qualitative and quantitative improvements on all the best previously known irrationality results for dilogarithms of positive rational numbers. We obtain such improvements by applying our permutation group method to the diophantine study of double integrals of rational functions related to the dilogarithm.
The Picard-Vessiot closure in differential Galois theory
The pi-separability of Certain Factorizable Groups.
The Poincaré Series of a Coxeter Group.
The Poisson formula for groups with hyperbolic properties.
The possibility of extending factorization results to infinite Abelian groups.
The p-period of an infinite group.
For Γ a group of finite virtual cohomological dimension and a prime p, the p-period of Γ is defined to be the least positive integer d such that Farrell cohomology groups Hi(Γ; M) and Hi+d(Γ; M) have naturally isomorphic ZΓ modules M.We generalize a result of Swan on the p-period of a finite p-periodic group to a p-periodic infinite group, i.e., we prove that the p-period of a p-periodic group Γ of finite vcd is 2LCM(|N(〈x〉) / C(〈x〉)|) if the Γ has a finite quotient whose a p-Sylow subgroup is elementary...
The prevalence of permutations with infinite cycles
A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category,...
The primitive distance-transitive representations of the Fischer groups.
The Primitive Permutation Groups of Some Special Degrees.
The Primitive Permutation Groups of Some Special Degrees, II: Small Multiples of Certain Large Primes.
The primitivity of semigroup algebras of free products.
The probability that elements of a rank free group generate a rank subgroup.
The product of generalized subnormal subgroups in finite groups.
The Profinite Completion of Certain Residually-Finite p-Groups.
The proof of Birman's conjecture on singular braid monoids.