On the dimension subgroups of metabelian groups. (English) Zbl 0482.20007
MSC:
| 20C07 | Group rings of infinite groups and their modules (group-theoretic aspects) |
| 20F16 | Solvable groups, supersolvable groups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20F14 | Derived series, central series, and generalizations for groups |
| 20F05 | Generators, relations, and presentations of groups |
| 20F12 | Commutator calculus |
Keywords:
integral dimension subgroup; lower central series; metabelian groups; finitely presented group; preabelian presentation; free group ring; augmentation idealsReferences:
| [1] | Gruenberg, K. W., Cohomological topics in group theory, (Lecture Notes in Mathematics No. 143 (1970), Springer: Springer Berlin-Heidelberg-New York) · Zbl 0205.32701 |
| [2] | Magnus, W., On a theorem of Marshall Hall, Ann. of Math. Ser. II, 40, 764-768 (1939) · JFM 65.0068.01 |
| [3] | Magnus, W.; Karrass, A.; Solitar, D., Combinatorial Group Theory (1966), Interscience: Interscience New York · Zbl 0138.25604 |
| [4] | Passi, I. B.S., Group rings and their augmentation ideals, (Lecture Notes in Mathematics No. 715 (1979), Springer: Springer Berlin-Heidelberg-New York) · Zbl 1028.20006 |
| [5] | Rips, E., On the fourth integer dimension subgroup, Israel J. Math., 12, 342-346 (1972) · Zbl 0267.20018 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
