We investigate the properties of Lie algebras of characteristic p which satisfy the Engel identity xy" = 0 for some n < p. We establish a criterion which (when satisfied) implies that if a and b are elements of an Engel-n Lie algebra L then abn~2 generates a nilpotent ideal of I. We show that this criterion is satisfied for n = 6, p = 1, and we deduce that if G is a finite m-generator group of ...

IN this paper we shall study the connection between local and global nilpotency for groups which satisfy certain chain conditions. In the first section, we shall prove that a group satisfying the chain condition on centralizers has a unique maximal normal nilpotent subgroup (the Fitting subgroup), i.e. the group generated by all normal nilpotent subgroups must again be nilpotent. This generaliz...

Recommended by Stéphane Louboutin Two kinds of series representations, referred to as the Engel series and the Cohen-Egyptian fraction expansions, of elements in two different fields, namely, the real number and the discrete-valued non-archimedean fields are constructed. Both representations are shown to be identical in all cases except the case of real rational numbers.

151. Margolin SG, Strauss H, Engel GL: Electroencephalographic changes associated with hypersensitivity of the carotid sinus. Arch Neurol Psychiatr 45:889-890, 1941 152. Engel GL, Margolin SG: Clinical correlation of the electroencephalogram with carbohydrate metabolism. Arch Neurol Psychiatr 45:890-891, 1941 153. Engel GL, Margolin SG: Neuropsychiatric disturbances in Addison's disease and the...

Let KG be the group ring of a group G over a field of characteristic p > 0, p ^ 2, 3. Suppose G contains no element of order p (if p > 0). Group algebras KG with unit group U(KG) solvable and n-Engel are characterized. Let ATG be the group ring of a group G over a field K of characteristic p > 0 and let U(KG) denote its group of units. Several authors including Bateman [1], Bateman and Coleman ...

We develop a construction of Engel structures on 4– manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4–manifolds admit an Engel structure. We also show that, given two Engel manifolds M1, M2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M1#M2#(S ×S) which is closely related to the ...

Recent molecular phylogenetic studies on Lophocoleaceae have recovered some well-supported monophyletic lineages within Chiloscyphus s. lat. that merit recognition at the generic level. As a consequence, Chiloscyphus is herein circumscribed to include only Chiloscyphus subgen. Chiloscyphus, Chiloscyphus subgen. Connati is elevated to generic rank to which the new name Cryptolophocolea is applie...