On groups with factorization. (English. Russian original) Zbl 0544.20021
Sov. Math., Dokl. 23, 19-22 (1981); translation from Dokl. Akad. Nauk SSSR 256, 26-29 (1981).
The author presents - without proofs - a series of results on finite groups G having subgroups A and B such that \(G=AB\) or \(G=ABA\). Amongst other things he obtains some non-simplicity criteria and characterizations of certain simple groups. Applying his techniques to infinite periodic groups he gets the following theorem: Let \(G=AB\) be a locally finite group, where A and B are nilpotent groups with finite commutator subgroups. Then G is solvable.
Reviewer: D.Held
MSC:
20D40 | Products of subgroups of abstract finite groups |
20E25 | Local properties of groups |
20F50 | Periodic groups; locally finite groups |
20D05 | Finite simple groups and their classification |
20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |