# Professor Anthony Gaglione

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

## Research Areas:

- Combinatorial group theory with applications to mathematical logic and cryptography

## Papers

- (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 for this paper.
- (with Ben Fine and Dennis Spellman) "Discriminating and Squarelike Groups II: Examples" (to appear in Houston J. Math.) PDF file

## Publications

**Textbooks, Monographs**- A. Gaglione, An Introduction to Group Theory, published by GPO, August 1992. Web version: An Introduction to Group Theory
- 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.
- 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- A. M. Gaglione and D. Spellman, "More model theory of free groups," accepted for publication in the Houston J. Math., 14 March 1994.
- 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.