DisCoMath Seminar: Binary Fano Plane and Automorphisms of Order 7
Discrete & Computational Math Seminar (DisCoMath)
Binary Fano Plane and Automorphisms of Order 7
Kristijan Tabak
RIT Croatia
Abstract:
The binary Fano plane is a combinatorial design embedded in 7-dimensional finite vector space over GF(2). The blocks are made of 3-dimensional subspaces so that any 2-dimensional space is a subspace of just one block. It is still unknown whether such a design exists. What is known is that (among others) an automorphism of order 7 can’t operate on a set of blocks. This was proved by extensive use of computer power.
Here we present the first algebraic computer-free proof of that fact. The methods used in the proof involve group theory, character theory and calculations in various group rings.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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