Periods of p-adic Schottky groups.
Periods of sets of lengths: a quantitative result and an associated inverse problem
The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...
Peripheral separability and cusps of arithmetic hyperbolic orbifolds.
Permutability of centre-by-finite groups
Let be a group and be an integer greater than or equal to . is said to be -permutable if every product of elements can be reordered at least in one way. We prove that, if has a centre of finite index , then is -permutable. More bounds are given on the least such that is -permutable.
Permutability of congruences on commutative semigroups.
Permutability of normal extensions of a semilattice.
Permutable duo semigroups.
Permutable groupoids
Permutable Subgroups of Infinite Groups.
Permutable transformation semigroups.
Permutation functions and (n,m)-commutativity of semigroups .
Permutation group extension of groupoids.
Permutation Groups of Even Degree Whose 2-Point Stabilisers are Isomorphic Cyclic 2-Groups.
Permutation modules and projective resolutions.
Permutation polynomials in several variables over finite fields
Permutation properties and the Fibonacci semigroup.
Permutations avoiding arithmetic patterns.
Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences
We are interested in permutations preserving certain distribution properties of sequences. In particular we consider -uniformly distributed sequences on a compact metric space , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group . We show that is big in the...
Permutations which make transitive groups primitive
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...
Permutations with Kazhdan-Lusztig polynomial . With an appendix by Sara Billey and Jonathan Weed.