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The Hughes subgroup

Robert Bryce (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let G be a group and p a prime. The subgroup generated by the elements of order different from p is called the Hughes subgroup for exponent p . Hughes [3] made the following conjecture: if H p ⁢ G is non-trivial, its index in G is at most p . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case p = 3 and G arbitrary, and that of Hogan and Kappe [2] concerning the case when G is metabelian, and p arbitrary. A common proof is...

The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

Alexander Rudy (2005)

Open Mathematics

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.

The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals

Antonio M. Peralta, Hermann Pfitzner (2015)

Studia Mathematica

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.

The Kuranishi space of complex parallelisable nilmanifolds

Sönke Rollenske (2011)

Journal of the European Mathematical Society

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.

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