We prove an upper bound on the minimal length of a factorization of a general finite group as a product of conjugate solvable subgroups which, for a large class of groups, is linear in the non-solvable length of G. We also show that every solvable group G is a product of at most 1+c log |G : C| conjugates of a Carter subgroup C of G, where c 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.
We consider factorizations of a finite group G into conjugate subgroups, G = Ax1⋯Axk for A ≤ G and x1,...,xk G, where A 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 G. We also show that every solvable group G is a product of at most 1 + clog|G: C| conjugates of a Carter subgroup C of G, where c 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.
Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent
Garonzi M;
2017
Abstract
We consider factorizations of a finite group G into conjugate subgroups, G = Ax1⋯Axk for A ≤ G and x1,...,xk G, where A 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 G. We also show that every solvable group G is a product of at most 1 + clog|G: C| conjugates of a Carter subgroup C of G, where c 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.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
