On the application of D. I. Moldavanskii’s method to the study of the approximability of HNN-extensions by root classes of groups
This is an expanded version of a paper read by the author at the International scientific conference dedicated to the 75th anniversary of Professor D. I. Moldavanskii (Ivanovo, 2015). The article provides an overview of the root classes and the approximability by them of free constructions of groups, a brief survey of the known results on the approximability (relatively to the relationship of elements equality) of nonascending HNN-extensions, and a description of some new results on the approximability by root classes of HNN-extensions with central associated subgroups including those obtained using D. I. Moldavanskii’s method of the descent and the ascent of compatible subgroups.