MY RESEARCH |
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My main research interests lie at the intersection of General (or Universal) Algebra and Group Theory. I am particularly interested in the interplay between ideas and tools from General Algebra and groups, and how the former may be used to solve problems in Group Theory. My research so far reflects these interests. My thesis and early work dealt with amalgams of nilpotent groups, and made strong use of dominions, a construction introduced by Isbell in a General Algebra context. It also explored the notion of epimorphism in varieties of groups. In more recent work, I have used many of the ideas (in particular, the nilpotent product, a type of coproduct) to investigate the very down-to-Earth group theoretic problem of capability of groups. Since the Summer of 2014, I have been working with Martha Kilpack (currently at SUNY Oneonta) on a question that combines lattice theory and group theory, namely, to characterize those group for which the closure operators on its subgroup lattice form a lattice isomorphic to the lattice of subgroups of some (possibly different) group. I have a summary of my results so far. I have several pages dealing with the background of my research. The more elaborate ones deal with Amalgams and dominions. I also have some pages on capability of groups and on the lattice of closure operators problem. Finally, a link to a list of relevant references. |
Last modified: July 30, 2003 avm1260@louisiana.edu |