38 citations · 194 across the 17 of their papers we have counts for
13 papers · 1 filter
Subgroups of simple groups are as diverse as possible
Martin Kassabov, Brady A. Tyburski, James B. Wilson
For a finite group , let be the number of subgroups of and the number of isomorphism types of subgroups of . Let denote a simple group of Lie…
Isomorphism testing of groups of cube-free order
Heiko Dietrich, James B. Wilson
A group has cube-free order if no prime to the third power divides . We describe an algorithm that given two cube-free groups and of known order, decides whether $…
Polynomial-time isomorphism testing of groups of most finite orders
Heiko Dietrich, James B. Wilson
[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers , isomorphis…
The threshold for subgroup profiles to agree is
James B. Wilson
For primes there are at least groups of order that have equal multisets of isomorphism types of proper subgroups and proper quotient groups, isomorph…
A fast isomorphism test for groups of genus 2
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited t…
Skolem-Noether for nilpotent products
James B. Wilson
We consider the structure of groups and algebras that can be represented as automorphisms or derivations of distributive products -- which includes nonassociative rings, modules, f…
New Lie products for groups and their automorphisms
James B. Wilson
We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a gr…
Longer nilpotent series
James B. Wilson
New nilpotent series are produced that refine the usual nilpotent series of a group. These refinements can be arbitrarily longer than the series they refine and therefore clarify i…
Groups acting on tensor products
Peter A. Brooksbank, James B. Wilson
Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and autom…
Isomorphism in expanding families of indistinguishable groups
Mark L. Lewis, James B. Wilson
For every odd prime and every integer there is a Heisenberg group of order that has pairwise nonisomorphic quotients of order $p^{n…
Finding direct product decompositions in polynomial time
James B. Wilson
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indec…
Finding central decompositions of p-groups
James B. Wilson
Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las…
Decomposing p-groups via Jordan algebras
James B. Wilson
For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset…