Abstract:
For a family of $(2k+1)$-valued groups ($k\ge 1$) of three elements, it is proven that a group from this family is a coset one if and only if $4k+3$ is a power of a prime number. The connection between coset multivalued groups with three elements and finite groups of rank $3$ is discussed.
Keywords:multivalued group, coset group, group of rank 3.
Citation:
I. N. Ponomarenko, “On a family of multivalued groups”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 311–313
\Bibitem{Pon24}
\by I.~N.~Ponomarenko
\paper On a family of multivalued groups
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 311--313
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4434}
\crossref{https://doi.org/10.4213/tm4434}