Search results for "Division algebras"
showing 3 items of 3 documents
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
2015
AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.
Groups described by element numbers
2013
Abstract Let G be a finite group and L e ( G ) = { x ∈ G ∣ x e = 1 } $L_e(G)=\lbrace x \in G \mid x^e=1\rbrace $ , where e is a positive integer dividing | G | $\vert G\vert $ . How do bounds on | L e ( G ) | $\vert L_e(G)\vert $ influence the structure of G? Meng and Shi [Arch. Math. (Basel) 96 (2011), 109–114] have answered this question for | L e ( G ) | ≤ 2 e $\vert L_e(G)\vert \le 2e$ . We generalize their contributions, considering the inequality | L e ( G ) | ≤ e 2 $\vert L_e(G)\vert \le e^2$ and finding a new class of groups of whose we study the structural properties.
Divisible designs from semifield planes
2002
AbstractWe give a general method to construct divisible designs from semifield planes and we use this technique to construct some divisible designs. In particular, we give the case of twisted field plane as an example.