Vol. 6, No. 1, 2008

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Double-Baer groups

Vikram Jha and Norman L. Johnson

Vol. 6 (2008), No. 1, 227–248
DOI: 10.2140/iig.2008.6.227
Abstract

We show that a double-Baer group implies the existence of a double-retraction in a translation plane with kernel containing a field K = GF(q). If the associated spread is in PG(3,q) then a lifted spread in PG(3,q2) admits a double-Baer group. The double-retraction group produces a maximal partial mixed partition of PG(3,q2) of lines and PG(3,q). This result is generalized and new examples of translation planes admitting double-Baer groups are given.

Keywords
Baer groups, subgeometry partitions, lifting
Mathematical Subject Classification 2000
Primary: 51E23
Secondary: 51A40
Milestones
Received: 28 January 2008
Accepted: 25 February 2008
Authors
Vikram Jha
Glasgow CALEDONIAN University
Glasgow
United Kingdom
Norman L. Johnson
University of Iowa
IA
United States