If G is a finitely generated profinite group then the verbal subgroup Gq is open. In a d-generator finite group every product of qth powers is a product of f(d, q) qth powers. 20E20, 20F20.

Familial factors and perinatal problems in idiopathic childhood epilepsy. D. H. Mellor, I. Lowit, and D. J. Hall introduced by G. Russell. Department of Child Health, University of Aberdeen. As part of a study of childhood epilepsy, 128 schoolchildren were identified who had been diagnosed as having epilepsy but who had no evidence of cerebral malformation, postneonatal brain damage, or abnorma...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group Td−2 on a subgroup of (SO(d-2) × R-invariance) group. E.g. at d=9 the subgroup is exceptional G2 gr...

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.

We prove that every 2d-regular unimodular random network carries an invariant Schreier decoration. Equivalently, it is the coset graph of subgroup free group F d . As a corollary we get graphing local isomorphic image coming from p.m.p. action

0