SL（2，q）的一个特征性质

本文证明了非单群系列ＳＬ（２，ｑ）（ｑ＝ｐ￣ｎ＞３）可以仅用其极大子群阶之集来刻划，从而得到了ＳＬ（２，ｑ）的一个特征性质．     

RESEARCH ANNOUNCEMENTS——Strong Discreteness of Subgroups of SL（2, Гn）

As in [1,6], let Гn be the n-dimensional Clifford group, i.e., the set of all elements in n-dimensional Clifford algebra An, which can be expressed as a finite product of non-zero-vertors and SL(2, Гn) denote the group of n-dimensional Clifford matrices A=(α b c d)which satisfy:     

The K-admissibility of SL(2, 5)

Let K be a field and let G be a finite group. G is K-admissible if there exists a Galois extension L of K with G=Gal(L/K) such that L is a maximal subfield of a central K-division algebra. We characterize those number fields K such that H is K-admissible where H is any subgroup of SL(2, 5) which contains a S ₂-group. The method also yields refinements and alternate proofs of some known results including the fact that A ₅ is K-admissible for every number field K.Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthdayThe first author was partly supported by NSF fellowship DMS-8601130; the second author was partly supported by NSF grant DMS-8806371.     

On the groups SL2(ℤ[x]) and SL2(k[x,y])

This paper studies free quotients of the groups SL₂(ℤ[x]) and SL₂(k[x, y]),k a finite field. These quotients give information about the relation of the above groups to their subgroups generated by elementary or unipotent elements.     

Strong Uniform Expansion in SL(2, p)

We show that there is an infinite set of primes ${\mathcal P}We show that there is an infinite set of primes P{\mathcal P} of density one, such that the family of all Cayley graphs of SL(2, p), p ? P,{p \in \mathcal P,} is a family of expanders.     

SL(2,R)上的Hardy-Littlewood极大函数

给出了SL(2 ,R)上的Hardy Littlewood极大函数mf 和局部Hardy Littlewood极大函数mRf 的定义 ,对f∈L1(G) ,我们得到了 | {g∈SL(2 ,R) |mf(g) >λ} |的估计 ,且证明了局部Hardy Littlewood极大函数的弱(1.1)型和强 (p ,p)型 ,p >1.     

2-Cohomologies of the groups SL(n, q)

Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S²(V) be its symmetric square. We construct a 2-cohomology group H²(G, L). The group is one-dimensional over F _q if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H²(G, L) = 0. Previously, such groups H²(G, L) were known for the cases where n = 2 or q = p is prime. We state that H²(G, L) are trivial for n ⩾ 3 and q = p^m, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods. __________ Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008.     

Die irreduziblen Darstellungen der Gruppen SL2(Zp), insbesondere SL2(Z2). I. Teil

Ohne Zusammenfassung Unterstützt durch den Schweizerischen Nationalfonds (820.167.73).     

Die irreduziblen Darstellungen der Gruppen SL2(Zp), insbesondere SL2(Z2). II. Teil

Ohne Zusammenfassung Unterstützt durch den Schweizerischen Nationalfonds (820.167.73).     

Eisenstein series for SL(2)

This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL₂. They are used to compute both the value and derivatives of these functions at critical points.     

Raghunathan’s conjectures for SL(2,R)

In this paper I give simple proofs of Raghunathan’s conjectures for SL(2,R). These proofs incorporate in a simplified form some of the ideas and methods I used to prove the Raghunathan’s conjectures for general connected Lie groups. Partially supported by the NSF Grant DMS-8701840.