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A note on hypervector spaces

Sanjay Roy, Tapas K. Samanta (2011)

Discussiones Mathematicae - General Algebra and Applications

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

A note on infinite a S -groups

Reza Nikandish, Babak Miraftab (2015)

Czechoslovak Mathematical Journal

Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an a S -group. We study some properties of a S -groups. For instance, it is shown that a nilpotent group G is an a S -group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an a S -group which satisfies the descending chain condition on subgroups, then G is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an a S -group....

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

Let Q be a loop such that | Q | is square-free and the inner mapping group I ( Q ) is nilpotent. We show that Q is centrally nilpotent of class at most two.

Currently displaying 321 – 340 of 984