Pregled bibliografske jedinice broj: 264743
Block designs and strongly regular graphs constructed from the group U(3, 4)
Block designs and strongly regular graphs constructed from the group U(3, 4) // Glasnik matematički, 41 (2006), 2; 189-194 (međunarodna recenzija, članak, znanstveni)
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Naslov
Block designs and strongly regular graphs constructed from the group U(3, 4)
Autori
Crnković, Dean ; Mikulić, Vedrana
Izvornik
Glasnik matematički (0017-095X) 41
(2006), 2;
189-194
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
unitary group; block design; projective plane; Steiner system; strongly regular graph
Sažetak
We show a construction of the projective plane PG(2, 16) and the Hermitian unital S(2, 5, 65) from the unitary group U(3, 4). Further, we construct two block designs, a 2-(65, 15, 21) design and a 2-(65, 26, 250) design, and two strongly regular graphs with parameters (208, 75, 30, 25) and (416, 100, 36, 20). These incidence structures are defined on the elements of the conjugacy classes of the maximal subgroups of U(3, 4). The group U(3, 4) acts transitively as an automorphism group of the so constructed designs and strongly regular graphs. The strongly regular graph with parameters (416, 100, 36, 20) has the full automorphism group of order 503193600, isomorphic to G(2, 4):Z_2. Since the Janko group J_2 is a subgroup of G(2, 4), J_2 acts as an automorphism group of the constructed SRG(416, 100, 36, 20).
Izvorni jezik
Engleski
Znanstvena područja
Matematika
