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Generalized j-planes


Abstract


We construct and study a class of translation planes with kernel K\cong GF(q), order q^n, and n>2. These planes generalize the j-planes discovered by Johnson, Pomareda and Wilke in [14]. We show these planes are actually jj \cdots j-planes. Hence, most of the results obtained in this article are on jj\cdots j-planes. In fact, our study shows that these planes are either nearfield or new.

An infinite class of nearfield jj\cdots j-planes is shown to exist, and a finite set of sporadic non-Andr\'e jj\cdots j-planes is presented.


DOI Code: 10.1285/i15900932v29n2p143

Keywords:
Translation planes, homology groups, nets, j-planes

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