Note on Caranti's method of construction of Miller groups (Q1692330)

The authors are interested in constructing examples of finite non-abelian $p$-groups whose automorphism group is abelian -- they call such groups Miller groups. Most known examples are special $p$-groups and in the paper under review the aim is to obtain examples of non-special Miller groups from special Miller groups. This is done by altering a technique devised by \textit{A. Caranti} [Isr. J. Math. 205, 235--246 (2015; Zbl 1322.20014)]. \par The main results are four theorems that produce examples of non-special Miller $p$-groups as amalgamated semi-direct products of a special Miller $p$-group by a cyclic $p$-group subjected to further technical conditions.