On The Lattice Of Subnormal Subgroups Of Matrix Groups

Authors

  • A. Vethamanickam
  • R .Rosie Gracia

Keywords:

Subnormal subgroups, Almost subnormal subgroups

Abstract

In this paper we give the lattice structure of the lattice of subnormal subgroups of the group of  2 x 2 matrices over ZP , having determinant value 1, under matrix multiplication modulo p ,where is a prime number and p=2,3. The properties satisfied are modular, dually semi modular and consistent                                                                                                 

We also introduce the concept of almost subnormal subgroups of a group G and we give the lattice structure of the lattice of almost subnormal subgroups of the above mentioned group when p= 2, 3, 5 and 7.

The motivation for this study is the paper ‘Consistent Dually Semi modular lattices’ by Karen M. Gragg and Joseph P.S Kung, Journal of Combinatorial Theory, Series A 60,246-263(1992)

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References

Rosenfeld . A ., Fuzzy groups , J. Math Anal and App.35(1971), 512-517.

Ralph N.Mckenzie,George E. Merulty,Walter F.Taylor,Algebras,Lattices,Varieties,Volume I,Wadsworth and Brooks/cole,Monetary California, 1987.

Stanley R.P , Supersolvable lattice , Algebra Universalis,4(1974), 361-371.

Chajda , I., Radeleczki , S., 0 – conditions and Tolerance schemes, Acta Math. Univ.Comeniance , LXX11,2, 177-184(2003).

I.N.Herstein , Topics in Algebra , Second edition John Willey & Sons, New York, 1975.

Consistent Dually Semimodular Lattices by Karen M . Gragg and Joseph P.S. Kung , Journal of combinatorial theory, series A 60, 246 – 263(1992).

D . Jebaraj Thiraviam , A study on some special types of lattices, Ph.D thesis , Manonmaniam Sundaranar University,(2015).

Vethamanickam. A, Topics in universal Algebra, PhD .thesis, Madurai Kamaraj University , 1994.

R. Dedekind. Uber die Anzahl der Ideal-Classen in den verschiedenen Ordnungen eines endlichen korpers. Festschrift zur Saecularfeier des Geburtstages von C.F Gauss, Vieweg, Braunschweig, 1877, 1-55; see Ges. Werke, BandI, Vieweg, Braunschweig, 1930, 105-157

Gratzer, G., Lattice theory: Foundation.Birkhauser Veslag, Basel, 1998.

Czedli, G., Horvath E.K and Radeleczki,S. On tolerance lattices of algebras in congruence modular varieties, Acta Math.Hungar. 100(1-2) (2003), 9 – 17.

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Published

2025-07-04

How to Cite

1.
Vethamanickam A, Gracia R .Rosie. On The Lattice Of Subnormal Subgroups Of Matrix Groups. J Neonatal Surg [Internet]. 2025Jul.4 [cited 2025Jul.20];14(32S):3555-60. Available from: https://jneonatalsurg.com/index.php/jns/article/view/7969

Issue

Vol. 14 No. 32S (2025): Journal of Neonatal Surgery

Section

Original Article

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