A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
Let the group G = AB be a product of two π-decomposable sub- π is a set of primes. The authors conjecture that Oπ(A)Oπ(B) = Oπ(B)Oπ (A) if π is a set of odd primes. In this paper it is proved that the conjecture is true if A and B are soluble. A similar result with certain additional restrictions holds in the case 2 ∈ π. Moreover, it is shown that the conjecture holds if O π ′ (A) and O π ′ (B) have coprime orders. 2000 Mathematics Subject Classification. 20D20, 20D40. Conjecture. Let π be adoi:10.5565/publmat_53209_07 fatcat:3e3rykpzvzgxvmrbi45bxb5f7e