PROFESSOR A. M. GAGLIONE

Mathematical interests: Combinatorial group theory with applications to mathematical logic and cryptography

A conference in honor of Anthony Gaglione's 60th birthday
ASPECTS OF INFINITE GROUP THEORY

Dr. Gaglione's research is in the field of Combinatorial Group Theory. More specifically, he works in a sub-category of this field called the commutator calculus. This research has its origins in the work of Philip Hall, who invented the "Collection Process." This method and its applications mark the beginning of the commutator calculus. One of the principle applications of the collection process is the determination of the quotient groups of the lower central series of free groups of finite rank.
Recently, Dr. Gaglione has succeeded in determining "in principle" all quotient groups of the lower central series for a large class of groups. These groups are important in other areas of mathematics (e.g., algebraic topology) and also arise in many other applications. Should such a group arise in any application, it would be important to have a "description" of that group.
Dr. Gaglione has also been involved in applications of group theory to logic and to cryptography. Dr. Gaglione has numerous publications in this area.

Education: PhD, Polytechnic Univ (Brooklyn N.Y.), 1972

My office is in Chauvenet. If you want to make an appointment send email or call (410)293-6767.

Teaching

Policy statement for sm314
Syllabus for sm314
Practice final exam for sm314: pdf, and solutions pdf,

Here are some papers in group theory.

(with Dennis Spellman) "Does Lyndon's length function imply the universal theory of free groups?" copyright AMS 1994 (appeared in Contemp. Math. vol 169, 1994) (~22K)
The pdf file, ps file for this paper.
(with Ben Fine and Dennis Spellman) "Discriminating and Squarelike Groups II: Examples" (to appear in Houston J. Math.)
The pdf file, ps file.

Some publications:

Textbooks, Monographs
1. A. Gaglione, An Introduction to Group Theory, published by GPO, August 1992. Web version: An Introduction to Group Theory
2. B. Fine, A. Gaglione, F.C.Y. Tang, Proceedings of the AMS Combinatorial Group Theory Special Session held April 23-24, 1988, published by AMS in the Contemporary Mathematics Series, 1990.
3. R. Artino, A. Gaglione, N. Shell, The Contest Problem Book IV, published by the MAA in the New Mathematics Library, 1983.
Selected research articles in refereed journals
1. A. M. Gaglione and D. Spellman, "More model theory of free groups," accepted for publication in the Houston J. Math., 14 March 1994.
2. A.M. Gaglione and H.V. Waldinger, "Generalizations of commutator identities of Struik obtained through the Magnus algebra," the Houston J. Math., Vol. 20(1994), 201-236.

    address:  Department of Mathematics
              572C Holloway Road
              Annapolis, MD 21402
       email: amg@usna.edu
       phone: (410) 293-6767

"Material contained herein is made available for the purpose of peer review and discussion and does not necessarily reflect the views of the Department of the Navy or the Department of Defense."

Last updated: 2/16/2007 by wdj@usna.edu.