Frobenius Partitions in Extraspecial Groups |
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Authors: | N Gavioli V Pannone |
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Institution: | (1) Dipartimento di Matematica Pura ed Applicata, Università degli Studi, Via Vetoio, I-67010 Cioppito (L'Aquila), Italy;(2) Dipartimento di Matematica Ulisse Dini, Università degli Studi, Via Morgagni 67/A, I-50134 Firenze, Italy |
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Abstract: | Let K be a field and G be the group of the upper unitriangular (n + 2) × ( n + 2) K-matrices with nonzero entries only in the first row and in the last column. Then G has a normal subgroup N with a complement H which are K-vector spaces respectively of dimensions n + 1 and n. In the present paper we show that the orbit of H under a group of automorphisms of G together with N, forms a partition of G, provided that there exists a commutative (possibly nonassociative) division algebra of dimension n + 1 over K. This algebra exists when K is a finite field. |
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Keywords: | translation transversal designs partitions in finite groups communtative nonassociative division algebras |
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