A portrait of Poisson by B. Geller and Y. Bruk, Quantum, March/April 1991, pp21–25. - In search of a definition of surface area by V. Dubrovsky, Quantum March/April 1991, pp 6—9 and p 44. - Leopold Kronecker: a great gentleman in science by Hazel Perfect, Mathematical Spectrum 24 (1) pp 1–7. - An hour's conversation with Stepen Smale, by M. Wiggins. Nonlinear Science Today, 1(1) pp 1, 3 and 12–17. - Special issue on women in mathematics, Notices of the American Mathematical Society, 38 (70) pp701–777. - A perspective on computational number theory by R.D. Silverman. Notices of the American Mathematical Society, 38(6) pp562–568. - Number theory as gadfly by B. Mazur, American Mathematical Monthly, 98(7) pp 593–610. - Large-amplitude periodic oscillations in suspension bridges: some new connections with non-linear analysis by A.C. Lazer and P.J. Mckenna, SIAM review 32(4) pp 537–578. - Analysis of a model for complex skin patterns by L.J. Shaw and J.D. Murray, SIAM Journal on Applied Mathematics, 50(2) pp626–648. - Managing school mathematics departments: towards better practice, by Peter Earley and Felicity Fletcher-Campbell. Educational Research, 31(2)pp98–112.

1992 ◽  
Vol 76 (476) ◽  
pp. 325-327
Author(s):  
Steve Abbott
Keyword(s):  
Number Theory ◽  
Applied Mathematics ◽  
American Mathematical Society ◽  
Mathematical Society ◽  
Suspension Bridges ◽  
Siam Journal ◽  
Computational Number Theory ◽  
Definition Of ◽  
Siam Review ◽  
Women In Mathematics

scholarly journals NIELSEN EQUIVALENCE OF GENERATING PAIRS OF SL(2,q)

2013 ◽  
Vol 55 (3) ◽  
pp. 481-509 ◽  
Author(s):  
DARRYL MCCULLOUGH ◽  
MARCUS WANDERLEY
Keyword(s):  
Number Theory ◽  
American Mathematical Society ◽  
Equivalence Classes ◽  
Conjugacy Classes ◽  
Mathematical Society ◽  
Additional Work ◽  
Pure Math ◽  
Infinite Set

AbstractWe present several conjectures which would describe the Nielsen equivalence classes of generating pairs for the groups SL(2,q) and PSL(2,q). The Higman invariant, which is the union of the conjugacy classes of the commutator of a generating pair and its inverse, and the trace of the commutator play key roles. Combining known results with additional work, we clarify the relationships between the conjectures, and obtain various partial results concerning them. Motivated by the work of Macbeath (A. M. Macbeath, Generators of the linear fractional groups, in Number theory (Proc. Sympos. Pure Math., vol. XII, Houston, TX, 1967) (American Mathematical Society, Providence, RI, 1969), 14–32), we use another invariant defined using traces to develop algorithms that enable us to verify the conjectures computationally for all q up to 101, and to prove the conjectures for a highly restricted but possibly infinite set of q.

Sign in / Sign up

Export Citation Format

Share Document