Let p and q be two distinct prime ideals of Fq[T ]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curveX0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) with its subgroup generated by the cuspidal divisors, and to produce explicit examples of Jacquet-Langlands isogenies. Our results are stronger than what is currently known about the analogues of ...

We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry. We present some properties of the associated congruence subgroups. Namely, we show that a Hurwitz group defined by a congruence subgroup associated with an odd ideal, is necessarily defined by a principal congruence subgroup. All such Hurwitz gro...

Let IR(G) denote the augmentation ideal of the group algebra R(G) of a group G with coefficients in a commutative ring R . We give a complete description of the third relative dimension subgroup G∩ (1+ IR(K)IR(G)+ I3 R(G)) and the second relative Fox subgroup G ∩ (1 + IR(K)IR(H) + I2 R(G)IR(H)) for any subgroups K and H of G. Mathematical subjects classification: 20C07 (Primary), 20J05 (Seconda...

Let G ⊂ GL(V ) be a complex reductive group where dimV < ∞, and let π : V → V//G be the categorical quotient. Let N := ππ(0) be the null cone of V , and let H be the subgroup of GL(V ) which preserves the ideal I of N . We determine the identity component of H . For adjoint representations we determine H completely. We also investigate the subgroup GF of GL(V ) preserving a fiber F 6= N of π.

We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. W...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

Let G be a torsionfree compact p-adic analytic group. We give sufficient conditions on p and G which ensure that the Iwasawa algebra ΩG of G has no non-trivial two-sided reflexive ideals. Consequently, these conditions imply that every nonzero normal element in ΩG is a unit. We show that these conditions hold in the case when G is an open subgroup of SL2(Zp) and p is arbitrary. Using a previous...

Let O be the ring of integers of a totally real number field E and set G := ResE/Q(GL2). Fix an ideal c ⊂ O. For each ideal m ⊂ O let T (m) denote the mth Hecke operator associated to the standard compact open subgroup U0(c) of G(Af ). Setting X0(c) := G(Q)\G(A)/K∞U0(c), where K∞ is a certain subgroup of G(R), we use T (m) to define a Hecke cycle Z(m) ∈ IH2[E:Q](X0(c)×X0(c)). Here IH• denotes i...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.