Olga V. Kravtsova, Victoria O. Pramzina, “On collineation subgroup of semifield plane that isomorphic to <nobr>$A_4$</nobr>”, J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 4,Pages <nobr>498

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On collineation subgroup of semifield plane that isomorphic to $A_4$

Olga V. Kravtsova^a, Victoria O. Pramzina^b

^a Institute of Basic Training, Siberian Federal University, Krasnoyarsk, Russia
^b Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: It is proved that the translation complement of any semifield plane of rank 2 over finite field of odd order does not contain a collineaton subgroup isomorphic to $A_4$.

Keywords: semifield plane, translation complement, Baer involution, homolody.

UDC: 519.145

Received: 18.05.2011
Received in revised form: 25.06.2011
Accepted: 10.07.2011