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 |
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