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6 papers
A spectral theory for transverse tensor operators
Uriya First, Joshua Maglione, James B. Wilson
Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators an…
Exact sequences of inner automorphisms of tensors
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences…
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…
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 $…