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Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.

Subnormal, permutable, and embedded subgroups in finite groups

James Beidleman, Mathew Ragland (2011)

Open Mathematics

The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is subnormal....

Subtraction semigroups

Bohdan Zelinka (1995)

Mathematica Bohemica

A subtraction semigroup is a semigroup ( A , . , - ) with a further operation " - " added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.

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