1. Inherited unitals in Moulton planesGábor Korchmáros, Angelo Sonnino, Tamás Szőnyi, 2018, original scientific article Abstract: We prove that every Moulton plane of odd order-by duality every generalised André plane-contains a unital. We conjecture that such unitals are non-classical, that is, they are not isomorphic, as designs, to the Hermitian unital. We prove our conjecture for Moulton planes which differ from PG(2, q2) by a relatively small number of point-line incidences. Up to duality, our results extend previous analogous results-due to Barwick and Grünin-concerning inherited unitals in Hall planes.
Keywords: Unital, Moulton plane, Hermitian
Published in RUP: 19.12.2018; Views: 1969; Downloads: 158
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3. Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, original scientific article Abstract: A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Published in RUP: 03.04.2017; Views: 2533; Downloads: 87
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