DefinePK

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)