Tuval Foguel | Faculty Profiles | Adelphi University

Diplomas/Degrees

Ph.D., Mathematics, University of Illinois at Urbana-Champaign (1992)

B.S., Mathematics, York College of CUNY (1988)

Personal Statement

I am a Professor of Pure Mathematics, and my main research interests are in algebra.
I am a strong believer in the role of liberal education and its importance for all students. One of my favorite quotes that best describes the role of liberal art education comes from T.S. Eliot: “No one can become really educated without having pursued some study in which he took no interest. For it is part of education to interest ourselves in subjects for which we have no aptitude.”

Recent Courses

Abstract Algebra II

Bridge To Higher Mathematics

Calculus I

Number Theory

Research In Mathematics Covering Of Groups I

Research Interests

Group and Loop theory. Including coverings of groups and loops and the subloop lattice of finite loops.

International Experience

Organized Special session: Quasigroups, loops and applications during the Second Joint International Meeting of the Israeli Mathematical Union (IMU) and the American Mathematical Society (AMS) held in Tel-Aviv ISRAEL, June 16-19, 2014 (with Maria de Lourdes Merlini Giuliani, Michael Kinyon, J.D. Phillips, Liudmila Sabinina and Arye Juhász).

Organized the First Jamaican Conference on Group Theory and its Applications, Jan. 9 - 12, 1996, Mona, Jamaica (with J. Minty).

Lecturer in Mathematics Department of Mathematics, the University of the West Indies, Kingston, Mona, Jamaica (9/93- 7/97).

I also maintain ongoing collaboration with Baojun Li of Chengdu University of Information Technology in Chengdu, China. And with Dr Ali Reza Moghaddamfar of the K. N. Toosi University of Technology in Tehran, Iran.

Articles

Tuval Foguel, Josh Hiller (2020), A note on Abelian Partitionable groups, Communications in Algebra, 48, no.8, 3268-3274.

Tuval Foguel, Josh Hiller (2019), On Bruck's Prolongation and Contraction Maps, Quasigroups and Related Systems 27, 53-62.

Tuval Foguel, Nicholas Sizemore (2018), Partition Numbers of Finite Solvable Groups, Advances in Group Theory and Applications 6, 55-67.

Tuval Foguel and Josh Hiller (2016), A Note On Subloop Lattices. Results in Mathematics, 69, no.1, 11-21.

Tuval Foguel, Baojun Li (2015), On $\Pi$-property and $\Pi$-normality of subgroups of finite groups (II). Algebra and Logic, 54, No. 3, 211–225.

Risto Atanasov, Tuval Foguel (2014), Loops That Are Partitioned by Groups. Journal of Group Theory, 17, no. 5, 851–861.

Risto Atanasov, Tuval Foguel, Jeff Lawson (2013), Optimizing Capstone With Multiple Constraints. PRIMUS, 24, no.4, 392-402.

Risto Atanasov, Tuval Foguel, Andrew Penland (2013), Equal Quasi-Partition of p-groups. Results in Mathematics, 64, no.1, 85-191.

Risto Atanasov, Tuval Foguel (2012), Solitary solvable groups. Communications in Algebra, 40, no. 6, 2130-2139.

Tuval Foguel, Michael K. Kinyon (2010), Uniquely 2-divisible Bol loops. Journal of Algebra and Its Applications, 9, no. 4, 591-601.

Tuval Foguel (2008), Direct product of quasigroups and gd-subquasigroups. Quasigroups and Related Systems, 16, no. 1, 31-36.

Tuval Foguel, Joan Nunnelley Powell (2008), Fun with Cryptography: A Fun Workshop for Sonia Kovalevsky High School Mathematics Day. Geometry, Games, Graphs and Education: the Joe Malkevitch Festschrift, Comap, 165-172.

Tuval Foguel, Matthew Ragland (2008), Groups with a finite covering by isomorphic abelian subgroups. Contemporary Mathematics: Computational Group Theory and the Theory of Groups, 470, 75-88.

Tuval Foguel, Michael K. Kinyon, J.D. Phillips (2006), On twisted subgroups and Bol loops of odd order. Rocky Mountain Journal of Mathematics, 36, no.1, 183-212.

Tuval Foguel (2005), Associative transitive loops. Algebra Colloquium, 12, no. 3, 535-540.

Tuval Foguel (2005), A generalization of Supersolvability. Glasgow Mathematical Journal, 47, 249-253.

Tuval Foguel, Luise-Charlotte Kappe (2005), On loops covered by subloops. Expositiones Mathematicae, 23, 255 – 270.

Tuval Foguel, Pantelimon Stanica (2005), Almost Hamiltonian groups. Results in Mathematics 48 (2005), 48, 44-49.

Tuval Foguel (2005), Amalgam of a loop over an idempotent quasigroup. Quasigroups and Related Systems, 13, no. 1, 99-104.

Tuval Foguel (2004), Simple Power Associative Loops with Exactly One Covering. Results in Mathematics, 45, 241-245.

Tuval Foguel (2002), Polar Decomposition of Locally Finite Groups. Results in Mathematics, 42, 69-73.

Tuval Foguel, Abraham A. Ungar (2001), Gyrogroups and the Decomposition of Groups into Twisted Subgroups and Subgroups. Pacific Journal of Mathematics, 197, no. 1, 1-11.

Tuval Foguel, Abraham A. Ungar (2000), The Involutory Decomposition of Groups into Twisted Subgroups and Subgroups. Journal of Group Theory, 3, no.1, 27-4.

Tuval Foguel (2000), Groups, Transversals, and Loops. omment. Math. Univ. Carolinae, 41, no. 2, 261-269.

Tuval Foguel (1999), Groups with all Cyclic subgroups Conjugate - Permutable. Journal of Group Theory, 2, no.1, 47-52.

Tuval Foguel (1997), Conjugate - Permutable Subgroups. Journal of Algebra, 191, 235-239.

Tuval Foguel (1996), Simple Groups Containing Subgroups with some Normality Condition. Proceedings of the First Jamaican Conference on Group Theory and its Applications, 59-63.

Tuval Foguel (1996), On normal-composition series with simple nonabelian factors. Caribbean J. Math. Comput. Sci., 6, no. 1-2, 19-22.

Tuval Foguel (1995), Finite Groups with a Special 2-Generator Property. Pacific Journal of Mathematics, 170, no. 2, 483-496.

Tuval Foguel (1994), On Seminormal Subgroups. Journal of Algebra, 165, no. 3, 633-636.

Tuval Foguel (1993), Addendum to Galois-Theoretical Groups. Journal of Algebra, 157, no. 2, 574.

N. Boston, W. Dabrowski, Tuval Foguel, P.J. Gies, D.A. Jackson, J. Leavitt, D.T. Ose (1993), The Proportion of Fixed-Point-Free Elements of a Transitive Permutation Group. Communications in Algebra, 21, no. 9, 3259-3275.

Tuval Foguel (1992), Galois-Theoretical Groups. Journal of Algebra, 50 , no. 2, 321-323.

Professional Activities

Conferences Organized

1. 2016 Zassenhaus Group Theory Conference, June 10-12, 2016, Adelphi University, Garden City, NY (with Christopher K. Storm and Elizabeth Wilcox).

2. Special session: Quasigroups, loops and applications during the Second Joint International Meeting of the Israeli Mathematical Union (IMU) and the American Mathematical Society (AMS) to be held in Tel-Aviv ISRAEL, June 16-19, 2014 (with Maria de Lourdes Merlini Giuliani, Michael Kinyon, J.D. Phillips, Liudmila Sabinina and Arye Juhász).

3. 2013 Zassenhaus Group Theory Conference, May 24-26, 2013, Western Carolina University, Cullowhee, NC (with Risto Atanasov).

4. 2005 Zassenhaus Group Theory Conference, March 18-20, 2005, Auburn University Montgomery, Montgomery, Alabama (with Pante Stanica).

5. Special Session on Quasigroups and Loops at the Fall Eastern Sectional Meeting of the American Mathematical Society (AMS) in Binghamton, N.Y., Oct. 11-12, 2004 (with J. D. Phillips).

6. The First Jamaican Conference on Group Theory and its Applications, Jan. 9 - 12, 1996, Mona, Jamaica (with J. Minty).