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ON THE 2-NILPOTENT MULTIPLIER OF FINITE p-GROUPS

Published online by Cambridge University Press:  22 December 2014

PEYMAN NIROOMAND  and
MOHSEN PARVIZI
PEYMAN NIROOMAND
Affiliation:
School of Mathematics and Computer Science, Damghan University, Damghan 36715-364, Iran e-mail: niroomand@du.ac.ir, p_niroomand@yahoo.com
MOHSEN PARVIZI
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad 91775, Iran e-mail: parvizi@math.um.ac.ir
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Abstract

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The purpose of this paper is a further investigation on the 2-nilpotent multiplier, $\mathcal{M}$(2)(G), when G is a non-abelian p-group. Furthermore, taking G in the class of extra-special p-groups, we will get the explicit structure of $\mathcal{M}$(2)(G) and will classify 2-capable groups in that class.

Keywords

20C2520D15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 201 - 210
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

REFERENCES

1.Baer, R., Representations of groups as quotient groups, I, II, and III, Trans. Am. Math. Soc. 58 (1945), 295–419.Google Scholar
2.Berkovich, Ya. G., On the order of the commutator subgroups and the Schur multiplier of a finite p-group, J. Algebra 144 (1991), 269–272.CrossRefGoogle Scholar
3.Beyl, F. R., Felgner, U. and Schmid, P., On groups occurring as center factor groups, J. Algebra 61 (1979), 161–177.Google Scholar
4.Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of non-abelian tensor products of groups, J. Algebra 111 (1987), 177–202.Google Scholar
5.Brown, R. and Loday, J.-L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311–335.Google Scholar
6.Burns, J. and Ellis, G., On the nilpotent multipliers of a group, Math. Z. 226 (1997), 405–428.Google Scholar
7.Burns, J. and Ellis, G., Inequalities for Baer invariants of finite groups, Can. Math. Bull. 41 (4) (1998), 385–391.Google Scholar
8.Ellis, G., Tensor products and q-crossed modules, J. London Math. Soc. 51 (2) (1995), 243–258.Google Scholar
9.Ellis, G., On the Schur multiplier of p-groups, Commun. Algebra 9 (1999), 4173–4177.Google Scholar
10.Ellis, G. and Wiegold, J., A bound on the Schur multiplier of a prime power group, Bull. Aust. Math. Soc. 60 (1999), 191–196.CrossRefGoogle Scholar
11.Hall, P., The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141.Google Scholar
12.Hall, P., Verbal and marginal subgroups, J. Reine Angew. Math. 182 (1940), 156–157.Google Scholar
13.Jones, M. R., Multiplicators of p-groups, Math. Z. 127 (1972), 165–166.Google Scholar
14.Jones, M. R., Some inequalities for the multiplicator of a finite group, Proc. Am. Math. Soc. 39 (1973), 450–456.Google Scholar
15.Karpilovsky, G., The Schur multiplier, London Math. Soc. Monographs, New Ser., Vol. 2 (Clarendon Press, Oxford, 1987).Google Scholar
16.Lue, A. S.-T., The Ganea map for nilpotent groups, J. London Math. Soc. 14 (1976), 309–312.CrossRefGoogle Scholar
17.Mashayekhy, B. and Moghaddam, M. R. R., Higher Schur multiplicator of a finite abelian group, Algebra Colloq. 4 (3) (1997), 317–322.Google Scholar
18.Mashayekhy, B. and Sanati, M. A., On the order of nilpotent multipliers of finite p-groups, Commun. Algebra 33 (7) (2005), 2079–2087.Google Scholar
19.Moghaddam, M. R. R., Some inequalities for the Baer invariant of a finite group, Bull. Iran. Math. Soc. 9 (1981), 5–10.Google Scholar
20.Moghaddam, M. R. R., On the Schur-Baer property, J. Aust. Math. Soc. Ser. A 31 (1981), 343–361.Google Scholar
21.Moghaddam, M. R. R., The Baer invariant of a direct product, Arch. Math. 33 (1980), 504–511.Google Scholar
22.Niroomand, P., On the order of Schur multiplier of non-abelian p-groups, J. Algebra 322 (2009), 4479–4482.CrossRefGoogle Scholar
23.Niroomand, P., The Schur multiplier of p-groups with large derived subgroup, Arch. Math. 95 (2010), 101–103.CrossRefGoogle Scholar
24.Zhou, X., On the order of Schur multipliers of finite p-groups, Commun. Algebra 1 (1994), 1–8.Google Scholar