chains

chains
In first course we studied normal subgroups . In this chapter
we will study it as chains ( series ) ,

Let ( G , * ) be group , any finite sequence of subsets of

{e } = H0 ? H1 ? H2 ? … ? Hn _ 1 ? Hn = G


is called CHAIN ( series ) where all (Hi ,*) are subgroups of the group G the

Integer n is called the LENGTH of the chain .


Also we will study the normal chains and the composition chains .

In cyclic groups . In the end of this lecture we will determine the
Number of the composition chains in some cyclic groups .