THE SCHUR MULTIPLIER OF PAIRS OF NONABELIAN GROUPS OF ORDER P4

Authors

  • Adnin Afifi Nawi Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Johor Bahru, Johor, Malaysia
  • Nor Muhainiah Mohd Ali Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Johor Bahru, Johor, Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia 81310 UTM Johor Bahru, Johor, Malaysia
  • Samad Rashid Department of Mathematics, Faculty of Science, Islamic Azad University, Firoozkooh Branch, Tehran, Iran

DOI:

https://doi.org/10.11113/jt.v78.7810

Keywords:

Schur multiplier, pair of groups, normal subgroup, nonabelian group

Abstract

Let (G,N)  be a pair of groups where G is any group and N is a normal subgroup of G, then the Schur multiplier of pairs of groups is a functorial abelian group. The notion of the Schur multiplier of pairs of groups is an extension from the Schur multiplier of a group G. In this research, the Schur multiplier of pairs of finite nonabelian groups of order p4, where p is an odd prime, is determined.  

References

Schur, J. 1904. Über die Darstellung der endlichen Gruppen durch gebrochen lineare Substitutionen. Journal für die reine und angewandte Mathematik. 127: 20–50.

Karpilovsky, G. 1987. The Schur Multiplier. Oxford: Clarendon Press.

Green, J. A. 1956. On The Number Of Automorphisms Of A Finite Group. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 237(1211): 574–581.

Ok, K. S. 2001. On p-groups of order p4. Communications Korean Mathematical Society. 16(2): 205–210.

Ellis, G. 1998. The Schur Multiplier Of A Pair Of Groups. Applied Categorical Structures. 6(3): 355–371.

Moghaddam, M. R. R., Salemkar, A. R. and Chiti, K. 2007. Some Properties On The Schur Multiplier Of A Pair Of Groups. Journal of Algebra. 312(1): 1–8.

Burnside, W. 1911. The Theory of Groups of Finite Order. (2nd ed.). London: Cambridge University Press.

Visscher, M. 1998. On the nonabelian tensor products of groups, PhD Dissertation, State University of New York at Binghamton.

Brown, R., Johnson, D. L. and Robertson, E. F. 1987. Some Computations Of Non-Abelian Tensor Products Of Groups. Journal of Algebra. 111(1): 177–202.

Mohammadzadeh, F., Hokmabadi, A. and Mashayekhy, B. 2013. On The Order Of The Schur Multiplier Of A Pair Of Finite P-Groups II. Int. Journal of Group Theory. 2(3): 1–8.

Downloads

Published

2016-03-09

How to Cite

THE SCHUR MULTIPLIER OF PAIRS OF NONABELIAN GROUPS OF ORDER P4. (2016). Jurnal Teknologi (Sciences & Engineering), 78(3-2). https://doi.org/10.11113/jt.v78.7810