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Quasiprimitivity and quasigroups

1999
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Bulletin of the Australian Mathematical Society
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It is well known that Q is a simple quasigroup if and only if Mlt Q acts primitively on Q. Here we show that Q is a simple quasigroup if and only if MltQ acts quasiprimitively on Q, and that Q is a simple right quasigroup if and only if RMlt Q acts quasiprimitively on Q. A quasigroup is set with a single binary operation, denoted by juxtaposition, such that in xy = z, knowledge of any two of x,y and z specifies the third uniquely. A right quasigroup is a set with a single binary operation whose

doi:10.1017/s0004972700033165
fatcat:kvlksxx2abfo5kevbe75i2p5je