Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T07:32:42.496Z Has data issue: false hasContentIssue false
  • English
  • Français

Inequalities for Baer Invariants of Finite Groups

Published online by Cambridge University Press:  20 November 2018

John Burns  and
Graham Ellis
John Burns
Affiliation:
Mathematics Department University College Galway Galway Ireland, email: graham.ellis@ucg.ie
Graham Ellis
Affiliation:
Mathematics Department University College Galway Galway Ireland, email: graham.ellis@ucg.ie
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

20C25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 385 - 391
Copyright
Copyright © Canadian Mathematical Society 1998

References

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), 501–516.Google Scholar
2. Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of nonabelian tensor products of groups. J.Algebra 111 (1987), 177–202.Google Scholar
3. Burns, J. and Ellis, G., On the nilpotent multipliers of a group. Math. Zeit. 226 (1997), 405–428.Google Scholar
4. Ellis, G., The nonabelian tensor product of finite groups is finite. J.Algebra 111 (1987), 203–205.Google Scholar
5. Ellis, G., On five well-known commutator identities. J. Austral. Math. Soc. Ser. A 54 (1993), 1–19.Google Scholar
6. Ellis, G., Bounds for the derived and Frattini subgroups of a prime power group. Proc. Amer.Math. Soc. 126 (1998), 2513–2523.Google Scholar
7. Ellis, G. and McDermott, A., Tensor products of prime power groups. J. Pure Appl. Algebra (to appear).Google Scholar
8. Fröhlich, A., Baer-invariants of algebras. Trans. Amer.Math. Soc. 109 (1963), 221–244.Google Scholar
9. Hall, M. and Senior, J. K., The groups of order 2n(n ≤ 6). Macmillan, 1964.Google Scholar
10. Jones, M. R., Some inequalities for the multiplicator of a finite group. Proc. Amer. Math. Soc. (3) 39 (1973), 450–456.Google Scholar
11. Jones, M. R., Some inequalities for the multiplicator of a finite group II. Proc.Amer.Math. Soc. (2) 45 (1974), 167–172.Google Scholar
12. Karpilovsky, G., The Schur multiplier. London Math. Soc. Monographs (N.S.) 2. Oxford University Press, New York, 1987.Google Scholar
13. Lue, A. S.-T., The Ganea map for nilpotent groups. J. London Math. Soc. 14 (1976), 309–312.Google Scholar
14. Moghaddam, M. R. R., Some inequalities for the Baer invariant of a finite group. Bull. Iranian Math. Soc. 9 (1981), 5–10.Google Scholar
15. Moghaddam, M. R. R., On the Schur-Baer property. J. Austral. Math. Soc. Ser. A 31 (1981), 343–361.Google Scholar
16. Wiegold, J., Multiplicators and groups with finite central factor-groups. Math. Zeit. 89 (1965), 345–347.Google Scholar