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Colorado State University

1. Maglione, Joshua. On automorphism groups of p-groups.

Degree: PhD, Mathematics, 2017, Colorado State University

We provide the necessary framework to use filters in computational settings, in particular for finitely generated nilpotent groups. The main motivation for this is to construct automorphisms of the group from derivations and Lie automorphisms of an associated Lie algebra. The key application of our work is a naively parallelizable algorithm to compute Aut(G), for finite p-groups G of exponent p. This algorithm comes as a consequence of several structure theorems on filters; one, which allows for parallelism, is a theorem about general decompositions of groups (e.g. central decompositions) and their automorphisms. Advisors/Committee Members: Wilson, James B. (advisor), Hulpke, Alexander (committee member), Penttila, Tim (committee member), Ross, Kate (committee member).

Subjects/Keywords: filters; p-groups; Lie algberas; automorphisms

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APA (6th Edition):

Maglione, J. (2017). On automorphism groups of p-groups. (Doctoral Dissertation). Colorado State University. Retrieved from

Chicago Manual of Style (16th Edition):

Maglione, Joshua. “On automorphism groups of p-groups.” 2017. Doctoral Dissertation, Colorado State University. Accessed July 18, 2019.

MLA Handbook (7th Edition):

Maglione, Joshua. “On automorphism groups of p-groups.” 2017. Web. 18 Jul 2019.


Maglione J. On automorphism groups of p-groups. [Internet] [Doctoral dissertation]. Colorado State University; 2017. [cited 2019 Jul 18]. Available from:

Council of Science Editors:

Maglione J. On automorphism groups of p-groups. [Doctoral Dissertation]. Colorado State University; 2017. Available from: