“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 765 |
|
| Abstract: | |
|
In [6], Bhattacharya and Mukherjee defined the notion of
θ-pair for a maximal subgroup of a finite group. They
proved that for any maximal subgroup M of a finite group G,
there exists a θ-pair related to M. In [11], Zhao
improved this result. He proved that for any maximal subgroup M
of a finite group G, there exists a normal maximal θ-pair
related to M.
In this paper we introduce the notion of nθ-maximal and
primitive nθ-maximal group. We show that for n=1,2,G is
nθ-maximal if and only if G is primitive
nθ-maximal. Also, we characterize the 1θ-maximal
group and prove some results about 2θ-maximal groups.
Finally, we introduce the notion of nθ-pair group and prove
that for all n ≠ 2,3, there exists nθ-pair groups and
for n=2,3 there is no nθ-pair groups.
Download TeX format |
|
| back to top | |
