We shall say that an automorphism a is nilpotent or acts nilpotently on a group G if in the holomorph H= [G](a) of G with a, a is a bounded left Engel element, that is, [H, ¿a] = l for some natural number ¿. Here [H, ka] means [H, (k — l)a] with [H, Oa] denoting H. Let G' denote the commutator subgroup [G, G], and let $(G) denote the Frattini subgroup of G. If a is an automorphism of a nilpoten...

Replacement of cement with supplementary cementitious materials (SCMs) is a proven method to reduce clinker in and contribute decreased CO2 emissions. Natural clays are commonly occurring that do not possess pozzolanic activity their original state. Mechanochemical activation (MCA) can be an alternative sustainable enhance reactivity. In this study, the reactivity three natural clays, originati...

purpose : to describe a case of acute angle-closure glaucoma associated with oral topiramate (topamax, aria daroo) therapy case report: two weeks after initiation of oral topiramate therapy for epilepsy, a 35-year-old woman presented with blurred vision and headache. intraocular pressure in both eyes was significantly elevated and her visual acuity was 20/30 ocular uterque (ou). bilateral conju...

oro-antral communication and fistula can occur as a result of inadequate and improper treatment. inadvertent communication with the maxillary sinus can occur during certain surgical procedures in the maxillary posterior region. though, spontaneous healing may occur in defects which are smaller than 2 mm but larger communications require immediate attention and should be treated without delay, i...

background pilonidal disease is a common condition that affects younger people in which over half of the affected patients present with a sacrococcygeal abscess. this study was performed to compare the outcome of excision and primary closure with that of rhomboid excision and flap procedure in patients with uncomplicated pilo­nidal disease. methods a total of 90 consecutive patients with piloni...

Modular towers, a notion due to M. Fried, are towers of Hurwitz spaces, with levels corresponding to the characteristic quotients of the p-universal Frattini cover of a fixed finite group G (with p a prime divisor of |G|). The tower of modular curves X1(pn) (n>0) is the original example: the group G is then the dihedral group Dp. There are diophantine conjectures on modular towers, inspired by ...

Let p be a prime, P a finite non-cyclic p-gvoup and (xd)Q>(P) of the factor group P/$(P), and the map 61-+B is a homomorphism from the automorphism group Aut P of P to the automorphism group of P/$(P). When P/O(P) is regarded as a vector space over the field of order p, the restric...

We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-di...