Journal ArticleDOI
A New Class of Translation Planes Constructed by Hyper-regulus Replacement
Vikram Jha,Norman L. Johnson +1 more
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A new class of translation planes of order qn that admit very small affine homology groups is constructed by the replacement of a new hyper-regulus that cannot be an Andre or generalized Andre.Abstract:
A new class of translation planes of order qn that admit very small affine homology groups is constructed These planes are constructed by the replacement of a new hyper-regulus that cannot be an Andre hyper-regulus Hence, the planes cannot be Andre or generalized Andreread more
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Translation planes constructed by multiple hyper-regulus replacement
Vikram Jha,Norman L. Johnson +1 more
TL;DR: In this paper, a new class of mutually disjoint hyper-reguli of order q ≥ 2 and order n ≥ 2, for n > 2, is determined, which are not Andre or generalized Andre if n > 3.
Journal ArticleDOI
Scattered linear sets in a finite projective line and translation planes
TL;DR: In this article , a similar construction of a translation plane Af obtained from any scattered linearized polynomial f(x) in Fqt[x] is described and investigated, and a class of quasifields giving rise to such planes is defined.
Journal ArticleDOI
Planes and processes
TL;DR: All non-translation planes are described, fundamental processes in translation planes are defined and some of these are used to connect semi-field flocks with symplectic spreads and multiple hyper-regulus replacement are considered.
A standard form for scattered linearized polynomials and properties of the related translation planes
TL;DR: In this paper , the stabilizer G f of the subspace U f = { ( x, f ( x )): x ∈ F q n } , f( x ) a scattered linearized polynomial in F Q n [ x ], under the action of GL(2 , q n ).
Infinite hyper-regulus Sperner spaces
Vikram Jha,Norman Johnson +1 more
TL;DR: In this article, new constructions of infinite hyper-reguli are given, which produce a variety of new translation planes and Sperner spaces, as well as infinite hyperreguli with infinite translation planes.
References
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Journal ArticleDOI
Circle geometry in higher dimensions. II
TL;DR: In this paper, a definition of a d-dimensional circle-geometry for each integer d ≥ 2 is presented, and the definition is framed in such a manner that the circle geometries of dimension 2 are precisely the inversive planes.
Journal ArticleDOI
Translation planes constructed by multiple hyper-regulus replacement
Vikram Jha,Norman L. Johnson +1 more
TL;DR: In this paper, a new class of mutually disjoint hyper-reguli of order q ≥ 2 and order n ≥ 2, for n > 2, is determined, which are not Andre or generalized Andre if n > 3.
Journal ArticleDOI
Subregular Spreads of PG (5, 2e)
TL;DR: The theory of subregular spreads of PG(3,q) was developed by R.H. Bruck as discussed by the authors, and examples of such spreads were only constructed in PG(5, q) for q odd, where q is even.
Journal ArticleDOI
Lifting Subregular Spreads
TL;DR: In this article, it was shown that for every odd integer s ≥ 1, there is a corresponding set of mutually disjoint reguli in any Desarguesian plane, such that the line intersection properties of the reguli of S ≥ 1 are inherited from those of K ≥ 2.
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Translation planes constructed by multiple hyper-regulus replacement
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