Ph.D.: 1998, University of California at Berkeley
Matemático: 1993, Universidad Nacional Autónoma de México
I got my PhD from the University of California at Berkeley in 1998, working under George M. Bergman; I started at UL Lafayette in 2005. My main research interest is in groups. A group is a type of structures that were first defined to study symmetries, and are ubiquitous. The type of questions I am interested in are inspired by a viewpoint that comes from General (also called Universal) Algebra, which is a way of unifying the study of many different types of algebraic structures. In more recent years, I have concentrated in finite p-groups and nilpotent groups in general. My most recent work (in collaboration with Martha Kilpack) goes back to General Algebra and considers questions of lattice and closure operators associated to groups and their subgroups.
Selected research publications:
- On the capability of finite groups of class two and prime exponent, Publ. Math. Debrecen, 85/3-4 (2014), pp. 309-337.
- Two generator p-groups of nilpotency class two and their conjugacy classes (with Azhana Ahmad and Robert F. Morse), Publ. Math. Debrecen, 81 no. 1-2 (2012), pp. 145-166, MR 2957506.
- Certain homological functors for 2-generator p-groups of class two (with Robert F. Morse), Computational Group Theory and the Theory of Groups II, Contemporary Mathematics vol. 511, pp. 127-166. American Mathematical Society, 2010. MR 2655297.
- Embedding p-groups of class two and prime exponent in capable and non-capable groups, Bull. Austral. Math. Soc., 79 (2009), pp. 303-308. MR 2496934.
- Computational Group Theory and the Theory of Groups. (Editor, with Luise-Charlotte Kappe and Robert F. Morse), Contemporary Mathematics vol. 470, American Mathematical Society 2008.
- Capability of nilpotent products of cyclic groups II, Journal of Group Theory, 10 no. 4 (2007), pp. 441-451, MR 2334753.
- Capability of nilpotent products of cyclic groups, J. Group Theory, 8, no. 4 (2005), pp. 341-452. MR 2152690.
- Gauss's Lemma for number fields (with David McKinnon), American Math. Monthly , 112 no.5 (2005), pp. 385-416, MR 2139573.
- Amalgams of nilpotent groups of class two, J. Algebra, 274 (2004), pp. 1-63, MR 2040861.
- Absolutely closed nil-2 groups, Algebra Universalis, 42 (1-2) (1999), pp. 61-77, MR 1736342.