Metafields and Description of Metabelian Groups without the Involutions

Sergey V. Larin

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev, Krasnoyarsk, Russia

Abstract: The term quasifield is introduced for the description of metabelian groups but it also bears an independent meaning. It is proved that any finally generated metabelian group contains a generating set compared to which any element has a uniquely represented record. The elements of a group are multiplied under the formula that is defined by a characteristic numerical set. In addition, the characteristic numerical set defines the group uniquely up to isomorphisms.

Keywords: metabelian group, involution, metafield, isomorphism.

UDC: 512.5

Received: 18.02.2009
Received in revised form: 20.03.2009
Accepted: 20.04.2009