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About self-orthogonal \(n\)-groups. (English) Zbl 0900.20172

Summary: Self-orthogonal \(n\)-groups (\(n\geq 3\)), i.e. \(n\)-groups with \(n\) orthogonal principal parastrophes are considered. It is proved that finite such \(n\)-groups are idempotent. The explicit form of self-orthogonal 3-groups and examples of self-orthogonal \(n\)-groups are given.

MSC:

20N15 \(n\)-ary systems \((n\ge 3)\)
05B15 Orthogonal arrays, Latin squares, Room squares
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