Factorized spread sets and translation planes with large homology groups

Abstract

Abstract In this note we construct some series of translation planes of order q 2 which possess two commuting homology groups of order q – 1 and (q + 1)(q – 1, 2) respectively. These translation planes can be considered as relatives of nearfield planes: for nearfield planes the nontrivial part of the associated spread set is a group whereas in our case this set is the product of two groups.