A classification of regular \(p\)-groups with invariants \((e,2,1)\)
Elements \(b_1,\dots,b_r\) are said to form a \(U\)-basis of a finite \(p\)-group \(G\) if every element of \(G\) has a unique representation as a product \(b_1^{k_1}\cdots b_r^{k_r}\), where \(0\leq k_i<|b_i|\). By P.~Hall's theorem every regular \(p\)-group \(G\) has a \(U\)-basis and the set of orders of its elements is an invariant of \(G\), called \(e\)-invariants. The present paper contains a complete classification (up to isomorphism) of regular \(p\)-groups with \(e\)-invariants \(\{n,2,1\}\).
scientific article; zbMATH DE number 1747996