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Let be a group and a prime. The subgroup generated by the elements of order different from is called the Hughes subgroup for exponent . Hughes [3] made the following conjecture: if is non-trivial, its index in is at most . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case and arbitrary, and that of Hogan and Kappe [2] concerning the case when is metabelian, and arbitrary. A common proof is...
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.
We show that the deformation space of complex parallelisable nilmanifolds can be described
by polynomial equations but is almost never smooth. This is remarkable since these manifolds
have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
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