Аннотация:
Let $p$ be a prime number. Denote by $\mathfrak{R}_{\delta, \lambda}$ the non-abelian variety of nilpotent groups of class at most 2 of exponent $p^\delta$ with commutator subgroup of exponent $p^\lambda;$ by $F_2$ the free group of rank 2 in $\mathfrak{R}_{\delta, \lambda};$ by $qH$ the quasivariety of groups generated by a group $H.$ It is proved that the interval $[qF_2, qG]$ is continual if all the following conditions are true: $G\in\mathfrak{R}_{\delta, \lambda},$$G$ is a finite group defined in $\mathfrak{R}_{\delta, \lambda}$ by commutator defining relations, $qF_2\varsubsetneq qG.$
Полный текст:
PDF файл (492 kB)