Abstract
By a well-known result of Green (Proc R Soc A 237:574–581, 1956) and the formal definition of Ellis and Wiegold (Bull Austral Math Soc 60:191–196, 1999), there is an integer t, say corank(G), such that \({|\mathcal{M}(G)| = p^{\frac{1}{2}n(n-1)-t}}\). In Niroomand (J Algebra 322:4479–4482, 2009), the author showed for a non-abelian group G, corank(G) ≥ log p (|G|)−2 and classified the structure of all non-abelian p-groups of corank log p (|G|)−2. In the present paper, we are interesting to characterize the structure of all p-groups of corank log p (|G|)−1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berkovich Ya.G.: On the order of the commutator subgroups and the Schur multiplier of a finite p-group. J. Algebra 144, 269–272 (1991)
Ellis G.: On the Schur multiplier of p-groups. Comm. Algebra 27(9), 4173–4177 (1999)
Ellis G., Wiegold J.: A bound on the Schur multiplier of a prime power group. Bull. Austral. Math. Soc. 60, 191–196 (1999)
Green J.A.: On the number of automorphisms of a finite group. Proc. R. Soc. A 237, 574–581 (1956)
Jones M.R.: Multiplicators of p-groups. Math Z. 127, 165–166 (1972)
Jones M.R.: Some inequalities for the multiplicator of a finite group. Proc. Am. Math. Soc. 39, 450–456 (1973)
Karpilovsky, G.: The Schur multiplier, London Math. Soc. Monogr, New Series no.2, (1987)
Niroomand P.: On the order of Schur multiplier of non abelian p-groups. J. Algebra 322, 4479–4482 (2009)
Niroomand P.: The Schur multiplier of p-groups with large derived subgroup. Arch. Math. (Basel) 95(2), 101–103 (2010)
Zhou X.: On the order of Schur multipliers of finite p-groups. Commun. Algebra 1, 1–8 (1994)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by F. de Giovanni.
Rights and permissions
About this article
Cite this article
Niroomand, P. A note on the Schur multiplier of groups of prime power order. Ricerche mat. 61, 341–346 (2012). https://doi.org/10.1007/s11587-012-0134-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11587-012-0134-4