A note on groups of infinite rank whose proper subgroups are abelian-by-finite. (English) Zbl 1329.20041
B. Bruno and R. E. Phillips [Arch. Math. 65, No. 5, 369-374 (1995; Zbl 0857.20014)] proved that a non-perfect group with all proper subgroups nilpotent-by-finite is either nilpotent-by-finite or periodic. The ones that are not nilpotent-by-finite must also have infinite rank.
In this paper the following nice theorem is proved: Let \(G\) be a locally (soluble-by-finite) group of infinite rank whose proper subgroups of infinite rank are abelian-by-finite. Then all proper subgroups of \(G\) are abelian-by-finite.
In this paper the following nice theorem is proved: Let \(G\) be a locally (soluble-by-finite) group of infinite rank whose proper subgroups of infinite rank are abelian-by-finite. Then all proper subgroups of \(G\) are abelian-by-finite.
Reviewer: Martyn Dixon (Tuscaloosa)
MSC:
| 20F22 | Other classes of groups defined by subgroup chains |
