Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

Garonzi, Martino and Levy, Dan and Maróti, Attila and Simion, Iulian I. (2016) Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent. JOURNAL OF ALGEBRA AND ITS APPLICATIONS. pp. 1-17. ISSN 0219-4988

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Abstract

We consider factorizations of a finite group (Formula presented.) into conjugate subgroups, (Formula presented.) for (Formula presented.) and (Formula presented.), where (Formula presented.) is nilpotent or solvable. We derive an upper bound on the minimal length of a solvable conjugate factorization of a general finite group which, for a large class of groups, is linear in the non-solvable length of (Formula presented.). We also show that every solvable group (Formula presented.) is a product of at most (Formula presented.) conjugates of a Carter subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a positive real constant. Finally, using these results we obtain an upper bound on the minimal length of a nilpotent conjugate factorization of a general finite group. © 2017 World Scientific Publishing Company

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