On a maximality condition for subgroups of a locally solvable group. (Russian. English summary) Zbl 1441.20020
Summary: The author studies groups with restrictions on subgroups. He considers locally solvable groups with the maximal condition for subgroups. A subgroup of a locally solvable group is singled out, such that the fulfillment of the maximality condition for it implies the fulfillment of this condition on the entire group.
MSC:
20E15 | Chains and lattices of subgroups, subnormal subgroups |
20F16 | Solvable groups, supersolvable groups |
20F19 | Generalizations of solvable and nilpotent groups |
20E07 | Subgroup theorems; subgroup growth |
References:
[1] | Kargapolov M. I., Merzlyakov Yu. I., Foundations of group theory, 3rd edition, Nauka, M., 1982, 288 pp. (in Russian) · Zbl 0508.20001 |
[2] | Pontryagin L. S., Continuous groups, Nauka, M., 1984, 520 pp. (in Russian) · Zbl 0534.22001 |
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