Abstract
In this paper we will determined all of the primitive and imprimitive Soluble Subgroups of GL(4,pk). It turns out that the number of types of the irreducible Soluble Subgroups in GL(4,pk)are 10 types and are Mi,i=1,…,10. moreover we find these subgroups.
Highlights
Introduction and ElementaryDefinitions.in the early 1871 Jordan determined a table containing the number of conjugacy classes of maximal irreducible soluble subgroups of GL(n,p), for pn < 106.([6]) Dickson (1901, Chapter 12, pp. 260-287) determined all subgroups of PSp (2,pk) and in (1904) he determined all subgroups of PSp (4,3)
In the early 1871 Jordan determined a table containing the number of conjugacy classes of maximal irreducible soluble subgroups of GL(n,p), for pn < 106.([6]) Dickson (1901, Chapter 12, pp. 260-287) determined all subgroups of PSp (2,pk) and in (1904) he determined all subgroups of PSp (4,3)
In the early 1960 Sims developed an algorithm, based on coset enumeration, which takes as input a group G given by a finite representation and positive integer n, and output a list containing a representative of each conjugacy class of subgroups of G whose index is at most n
Summary
In the early 1871 Jordan determined a table containing the number of conjugacy classes of maximal irreducible soluble subgroups of GL(n,p), for pn < 106.([6]) Dickson Liskovec (1973) classified the maximal Irreducible (p,q)subgroups of GL (r2,p), where q and or are primes and q is odd. In the early 1960 Sims developed an algorithm, based on coset enumeration, which takes as input a group G given by a finite representation and positive integer n, and output a list containing a representative of each conjugacy class of subgroups of G whose index is at most n. In this paper we will determine the irreducible Soluble Subgroups of Gl(4,pk). For this purpose, we mention some Definitions and elementary notions.
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