2016/07/08 by Vahagn H. Mikaelian, Mikaelian, Vahagn H. · 1 citation
Computer Science · Engineering · Mathematics · #20D15 #20E10 #20E22 #20K01 #20K25 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1607.02464
openalex publication_date 2016/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We suggest a criterion under which for a nilpotent group of finite exponent A and for an abelian group B the variety var(A Wr B) generated by their wreath product A Wr B is equal to the product of varieties var(A) and var(B) generated by A and B. Namely the equality holds if and only if either the group B is not of some non-zero exponent; or if B is of a non-zero exponent n, and B contains a subgroup isomorphic to Cdc × Cn/d^∞, where c is the nilpotency class of A, d is the largest divisor of n coprime with m, Cdc is the direct power of c copies of the cycle Cd of order d, Cn/d^∞ is the direct power of countably many copies of the cycle Cn/d of order n/d. This criterion continues our previous work on cases when the similar criterions were given for wreath products of abelian groups or of finite groups. Also, this is a generalization of known results in literature, which solve the same problem for much more restricted cases. Some applications of the criterion are considered at the end of paper.