Minimal Non-Metabelian Varieties of โ-Groups Which Contain No Nonabeliano-Groups
Michael R. Darnel, W. Charles Holland ยท Communications in Algebra ยท 2014
Martinez suggested and Scrimger proved that, when n is prime, the varieties ๐ฎ n defined by what are now called Scrimger โ-groups S n cover the abelian variety, which is the smallest nontrivial variety of โ-groups. Darnel, Gurchenkov, and Reilly then independently proved that these are the only minimally nonabelian varieties which contain no nonabelian totally ordered groups. Holland and Reilly then gave a complete description of the lattice of metabelian โ-group varieties which contain no nonabelian totally ordered groups. This article now describes all of the minimally non-metabelian โ-group varieties which contain no nonabelian totally ordered groups.