Abstract:
There are several very useful formulas, which give the cycle
indices of
the binary operation of the sum, product, composition and po
wer group of
M
and
H
in terms of cycle indices of
M
and
H
. One very useful binary operation on groups,
which has not been exploited, is the semidirect product.
Suppose
G
=
M
⋊
H
, a semi direct product; the question is: how can we express
the cycle index of G in terms of the cycle indices of
M
and
H
? This work partially
answers this question by considering the cycle indices of so
me particularly semidirect
product groups; namely – Frobenious groups