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Inequalities for Baer Invariants of Finite Groups

  • John Burns (a1) and Graham Ellis (a1)

Abstract

In this note we further our investigation of Baer invariants of groups by obtaining, as consequences of an exact sequence of A. S.-T. Lue, some numerical inequalities for their orders, exponents, and generating sets. An interesting group theoretic corollary is an explicit bound for $|{{\gamma }_{c+1}}\,(G)|$ given that $G\,/\,{{Z}_{c}}\,(G)$ is a finite $p$ -group with prescribed order and number of generators.

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References

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1. Bacon, M. R. and Kappe, L.-C., The nonabelian tensor square of a 2-generator p-group of class 2. Arch. Math. 61 (1993), 501516.
2. Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of nonabelian tensor products of groups. J.Algebra 111 (1987), 177202.
3. Burns, J. and Ellis, G., On the nilpotent multipliers of a group. Math. Zeit. 226 (1997), 405428.
4. Ellis, G., The nonabelian tensor product of finite groups is finite. J.Algebra 111 (1987), 203205.
5. Ellis, G., On five well-known commutator identities. J. Austral. Math. Soc. Ser. A 54 (1993), 119.
6. Ellis, G., Bounds for the derived and Frattini subgroups of a prime power group. Proc. Amer.Math. Soc. 126 (1998), 25132523.
7. Ellis, G. and McDermott, A., Tensor products of prime power groups. J. Pure Appl. Algebra (to appear).
8. Fröhlich, A., Baer-invariants of algebras. Trans. Amer.Math. Soc. 109 (1963), 221244.
9. Hall, M. and Senior, J. K., The groups of order 2n(n ≤ 6). Macmillan, 1964.
10. Jones, M. R., Some inequalities for the multiplicator of a finite group. Proc. Amer. Math. Soc. (3) 39 (1973), 450456.
11. Jones, M. R., Some inequalities for the multiplicator of a finite group II. Proc.Amer.Math. Soc. (2) 45 (1974), 167172.
12. Karpilovsky, G., The Schur multiplier. London Math. Soc. Monographs (N.S.) 2. Oxford University Press, New York, 1987.
13. Lue, A. S.-T., The Ganea map for nilpotent groups. J. London Math. Soc. 14 (1976), 309312.
14. Moghaddam, M. R. R., Some inequalities for the Baer invariant of a finite group. Bull. Iranian Math. Soc. 9 (1981), 510.
15. Moghaddam, M. R. R., On the Schur-Baer property. J. Austral. Math. Soc. Ser. A 31 (1981), 343361.
16. Wiegold, J., Multiplicators and groups with finite central factor-groups. Math. Zeit. 89 (1965), 345347.
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Inequalities for Baer Invariants of Finite Groups

  • John Burns (a1) and Graham Ellis (a1)

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