37 citations · 54 across the 14 of their papers we have counts for
9 papers · 1 filter
Categorification of characteristic structures
Peter A. Brooksbank, Heiko Dietrich, Joshua Maglione +2
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing o…
Isomorphism invariant metrics
P. A. Brooksbank, J. F. Maglione, E. A. O'Brien +1
Within a category , having objects , it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic th…
Smooth cuboids in group theory
Joshua Maglione, Mima Stanojkovski
A smooth cuboid can be identified with a matrix of linear forms, with coefficients in a field , whose determinant describes a smooth cubic in the projective plane. T…
Enumerating isoclinism classes of semi-extraspecial groups
Mark L. Lewis, Joshua Maglione
We enumerate the number of isoclinism classes of semi-extraspecial -groups with derived subgroup of order . To do this, we enumerate -orbits of sets of irr…
Compatible filters with isomorphism testing
Joshua Maglione
Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central…
Efficient characteristic refinements for finite groups
Joshua Maglione
Filters were introduced by J.B. Wilson in 2013 to generalize work of Lazard with associated graded Lie rings. It holds promise in improving isomorphism tests, but the formulas intr…
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…
Automorphisms of small prime power groups
Joshua Maglione
If is the number of pairwise nonisomorphic groups of order , and is the number of groups of order whose automorphism group is a -group, then, for $…
Longer nilpotent series for classical unipotent subgroups
Joshua Maglione
In studying nilpotent groups, the lower central series and other variations can be used to construct an associated -graded Lie ring, which is a powerful method to ins…