The Schur multiplier of a nilpotent group
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- by Ursula Martin Webb
- Trans. Amer. Math. Soc. 291 (1985), 755-763
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800261-7
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Abstract:
In this paper we obtain upper and lower bounds for the rank of the Schur multiplier of a nilpotent group in terms of the nilpotency class and the number of generators and rank of the derived quotient.References
- I. V. Andožskiĭ, Certain classes of closed pro-$p$-groups, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 4, 707–738 (Russian). MR 0384944
- G. F. Bačurin, The multipliers of torsion-free nilpotent groups, Mat. Zametki 5 (1969), 541–544 (Russian). MR 251138
- N. Blackburn and L. Evens, Schur multipliers of $p$-groups, J. Reine Angew. Math. 309 (1979), 100–113. MR 542041
- W. Gaschütz and M. F. Newman, On presentations of finite $p$-groups, J. Reine Angew. Math. 245 (1970), 172–176. MR 271225, DOI 10.1515/crll.1970.245.172
- Karl W. Gruenberg, Cohomological topics in group theory, Lecture Notes in Mathematics, Vol. 143, Springer-Verlag, Berlin-New York, 1970. MR 0279200
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- A. I. Kostrikin, On defining groups by means of generators and defining relations, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 1119–1122 (Russian). MR 0199265
- Alexander Lubotzky, Group presentation, $p$-adic analytic groups and lattices in $\textrm {SL}_{2}(\textbf {C})$, Ann. of Math. (2) 118 (1983), no. 1, 115–130. MR 707163, DOI 10.2307/2006956
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory, Second revised edition, Dover Publications, Inc., New York, 1976. Presentations of groups in terms of generators and relations. MR 0422434
- Urs Stammbach, Homology in group theory, Lecture Notes in Mathematics, Vol. 359, Springer-Verlag, Berlin-New York, 1973. MR 0382477
- J. Wiegold, The Schur multiplier: an elementary approach, Groups—St. Andrews 1981 (St. Andrews, 1981) London Math. Soc. Lecture Note Ser., vol. 71, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 137–154. MR 679156
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 291 (1985), 755-763
- MSC: Primary 20J05; Secondary 20F18
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800261-7
- MathSciNet review: 800261