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Linear groups that are the multiplicative groups of neofields
Authors: Anthony B. Evans
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Abstract
A neofield $N$ is a set with two binary operations, addition and multiplication, for which $N$ is a loop under addition with identity $0$, the nonzero elements of $N$ form a group under multiplication, and both left and right distributive laws hold. Which finite groups can be the multiplicative groups of neofields? It is known that any finite abelian group can be the multiplicative group of a neofield, but few classes of finite nonabelian groups have been shown to be multiplicative groups of neofields. We will show that each of the groups $GL(n, q)$, $PGL(n, q)$, $SL(n, q)$, and $PSL(n, q)$, $q$ even, $q\ne 2$, can be the multiplicative group of a neofield.Wright State University
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Contents
- Valentin Belousov (20.02.1925 - 23.07.1988)
- Belousov's Theorem and the quantum Yang-Baxter equation
- Central and medial quasigroups of small order
- Algebras with Parastrophically Uncancellable Quasigroup Equations
- Linear groups that are the multiplicative groups of neofields
- On isotopies of some classes of Moufang loops
- Doubly transitive sets of even permutations
- Triality and Universal Multiplication Groups of Moufang Loops
- On paratopies of orthogonal systems of ternary quasigroups. I
- On cosets in Steiner loops
