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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The Schur multiplier of a nilpotent group


Author: Ursula Martin Webb
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
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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.


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  • [1] A. V. Andozhskii, On some classes of closed pro-$ p$ groups, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 707-738. MR 0384944 (52:5814)
  • [2] Y. Bacurin, The multipliers of torsion-free nilpotent groups, Mat. Zametki 5 (1969), 541-544. MR 0251138 (40:4369)
  • [3] N. Blackburn and L. Evens, Schur multipliers of $ p$-groups, J. Reine Angew. Math. 309 (1979), 100-113. MR 542041 (81a:20023)
  • [4] W. Gaschütz and M. Newman, On presentations of finite $ p$-groups, J. Reine Angew. Math. 245 (1970), 172-176. MR 0271225 (42:6108)
  • [5] K. W. Gruenberg, Cohomological topics in group theory, Lecture Notes in Math., vol. 143, Springer, Berlin, 1970. MR 0279200 (43:4923)
  • [6] B. Huppert, Endliche Gruppen, Springer, Berlin, 1967. MR 0224703 (37:302)
  • [7] A. I. Kostrikin, On presenting groups by generators and defining relations, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 1119-1122. MR 0199265 (33:7414)
  • [8] A. Lubotzky, Group presentation, $ p$-adic analytic groups and lattices in $ {\text{S}}{{\text{L}}_2}(\mathbf{C})$ (to appear). MR 707163 (85i:22017)
  • [9] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Dover, New York, 1976. MR 0422434 (54:10423)
  • [10] U. Stammbach, Homology in group theory, Lecture Notes in Math., vol. 359, Springer, Berlin, 1973. MR 0382477 (52:3360)
  • [11] J. Wiegold, The Schur multiplier: an elementary approach, Groups-St. Andrews 1981 (Eds., C. M. Campbell and E. Robertson), Cambridge Univ. Press, Cambridge, 1982. MR 679156 (84b:20001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0800261-7
Article copyright: © Copyright 1985 American Mathematical Society

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