On Conjugacy Classes of Sl(2, Q)
نویسنده
چکیده
Abstract. Let SL(2, q) be the group of 2× 2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of at least q − 1 distinct conjugacy classes of SL(2, q). On the other hand, if q > 3 is odd, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of at least q+3 2 distinct conjugacy classes of SL(2, q).
منابع مشابه
Q7-branes and their coupling to IIB supergravity
We show how, by making use of a new basis of the IIB supergravity axion-dilaton coset, SL(2,R)/SO(2), 7-branes that belong to different conjugacy classes of the duality group SL(2,R) naturally couple to IIB supergravity with appropriate source terms characterized by an SL(2,R) charge matrix Q. The conjugacy classes are determined by the value of the determinant of Q. The (p, q) 7-branes are the...
متن کاملThe Mckay Correspondence for Finite Subgroups of Sl(3,c)
Let G ⊂ SL(n, C) be a finite subgroup and φ:Y → X = C/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime divisors of Y correspond one-to-one with “junior” conjugacy classes of G. When n = 2 this is a version of the McKay correspondence (with irreducible representations of G replaced by conjugacy classes). In the case n = 3, a resolution with KY = 0 ...
متن کاملReal and strongly real classes in SL n ( q ) Nick Gill and Anupam Singh
We classify the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GLnðqÞ, SLnðqÞ, PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ.
متن کاملSquarefree Polynomials over Finite Fields and Regular Semisimple Classes of Certain Classical Groups
Let G be P SL n (q); P SU n (q); Sp 2n (q) or P Sp 2n (q), where q is a power of the prime p. Using results on the numbers of special squarefree polynomials over nite elds, we describe and count the conjugacy classes of p 0-elements with abelian centralizers in G. Similar results are obtained for the semisimple orbits of G on the corresponding nite Lie algebras.
متن کاملCONJUGACY CLASSES OF HYPERBOLIC MATRICES IN Sl(n, Z) AND IDEAL CLASSES IN AN ORDER
A bijection is proved between Sl( n, Z)-conjugacy classes of hyperbolic matrices with eigenvalues {A,,_A,,} which are units in an n-degree number field, and narrow ideal classes of the ring Rk = Z[A,]. A bijection between Gl(«,Z)-conjugacy classes and the wide ideal classes, which had been known, is repeated with a different proof. In 1980, Peter Sarnak was able to obtain an estimate of the gro...
متن کامل