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On equality of indices.

R.K.S. Rathore, H.L. Manocha (1973)

Publications de l'Institut Mathématique [Elektronische Ressource]

On Equational Theory of Left Divisible Left Distributive Groupoids

Přemysl Jedlička (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping a a 2 surjective lies in the variety generated by the left distributive left quasigroups.

On E-S-supplemented subgroups of finite groups

Changwen Li, Xuemei Zhang, Xiaolan Yi (2013)

Colloquium Mathematicae

The major aim of the present paper is to strengthen a nice result of Shemetkov and Skiba which gives some conditions under which every non-Frattini G-chief factor of a normal subgroup E of a finite group G is cyclic. As applications, some recent known results are generalized and unified.

On Exceptions in the Brauer-Kuroda Relations

Jerzy Browkin, Juliusz Brzeziński, Kejian Xu (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Let F be a Galois extension of a number field k with the Galois group G. The Brauer-Kuroda theorem gives an expression of the Dedekind zeta function of the field F as a product of zeta functions of some of its subfields containing k, provided the group G is not exceptional. In this paper, we investigate the exceptional groups. In particular, we determine all nilpotent exceptional groups, and give a sufficient condition for a group to be exceptional. We give many examples of nonnilpotent solvable...

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