SOME REMARKS ON H𝑣-GROUPS

  • Lee, Dong-Soo (Department Of Mathematics Chungnam National University) ;
  • Chung, Sang-Cho (Department Of Mathematics Chungnam National University)
  • Received : 2001.12.03
  • Published : 2001.12.31

Abstract

Vogiouklis introduced $H_v$-hyperstructures and gave the "open problem: for $H_v$-groups, we have ${\beta}^*={\beta}^{\prime\prime}$. We have an affirmative result about this open problem for some special cases. We study ${\beta}$ relations on $H_v$-quasigroups. When a set H has at least three elements and (H, ${\cdot}$) is an $H_v$-quasigroup with a weak scalar e, if there are elements $x,y{\in}H$ such that xy = H \ {e}, then we have (xy)(xy) = H.

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