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A property of the inverse of a subspace of a finite field

Sandro Mattarei

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Abstract

We prove a geometric property of the set A^{-1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new upper bound on the size of the intersection of A^{-1} with B when A and B are F_q-subspaces of different dimension of a finite field, satisfying a suitable assumption.

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What this paper is about

We prove a geometric property of the set A^{-1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new upper bound on the size of the intersection of A^{-1} with B when A and B are F_q-subspaces of different dimension of a finite field, satisfying a suitable assumption.

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Available abstract

We prove a geometric property of the set A^{-1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new upper bound on the size of the intersection of A^{-1} with B when A and B are F_q-subspaces of different dimension of a finite field, satisfying a suitable assumption.

Key concepts: Mathematics, Finite field, Subspace topology, Property (philosophy), Inverse, Field (mathematics), Pure mathematics, Algebra over a field

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