Groups with many subgroups of finite exponent. (English) Zbl 1116.20028
Mostly solvable groups with maximal or minimal condition for subgroups of infinite exponent are considered.
In the case of maximal condition the periodic groups are classified (Theorem 1(c)); in the case of minimal condition the groups are periodic and possess a normal subgroup of finite index and divisible commutator quotient group of finite rank (see Theorem 2).
In the case of maximal condition the periodic groups are classified (Theorem 1(c)); in the case of minimal condition the groups are periodic and possess a normal subgroup of finite index and divisible commutator quotient group of finite rank (see Theorem 2).
Reviewer: Hermann Heineken (Würzburg)
MSC:
| 20F16 | Solvable groups, supersolvable groups |
| 20F22 | Other classes of groups defined by subgroup chains |
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20F50 | Periodic groups; locally finite groups |
| 20E07 | Subgroup theorems; subgroup growth |
