ABSTRACT
A group whose elements are permutations on a given finite set of objects (symbols) is called a permutation group on these objects. Let a1, a2, . . . , an denote n distinct objects, and let b1, b2, . . . , bn be any arrangement of the same n objects. The operation of replacing each ai by bi, 1 ≤ i ≤ n, is called a permutation performed on the n objects. It is denoted by
S :
( a1 a2 · · · an b1 b2 · · · bn
) (B.1)
and is called a permutation of degree n. If the symbols on both lines in (B.1) are the same, the permutation is called the identical permutation and is denoted by I. Let
T :
( b1 b2 · · · bn c1 c2 · · · cn
) , U :
( a1 a2 · · · an c1 c2 · · · cn
) ,
then U is the product of S and T , i.e., U = ST , since
U = ST =
( a1 a2 · · · an b1 b2 · · · bn
)( b1 b2 · · · bn c1 c2 · · · cn
) =
( a1 a2 · · · an c1 c2 · · · cn
) .
