On varieties of $n$-solvable groups

V. M. Kotlov

National Taras Shevchenko University of Kyiv

Abstract: A new and shorter proof is given for the fundamental theorem of Kaluzhnin's recent note [1]: A variety of $n$-Abelian groups is the sum of a variety of Abelian groups and the respective Burnside varieties of groups of exponent $n$ and $1-n$. This theorem is extended to varieties of $n$-solvable groups.

UDC: 512.4

Received: 18.04.1968

 English version: Mathematical Notes, 1968, 4:6, 869–872

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