“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 7701 |
|
||||
| Abstract: | |||||
|
Let G be a finite group and OC(G) be the set of
order components of G. Denote by k(OC(G)) the number of
isomoporhism classes of finite groups H satisfying
OC(H)=OC(G). It is proved that some finite groups are uniquely
determined by their order components, i.e. k(OC(G))=1. Let
n=2m ≥ 4. As the main result of this paper, we prove that
if q is odd, then k(OC(Bn(q)))=k(OC(Cn(q)))=2 and if q
is even, then k(OC(Cn(q)))=1. A main consequence of our
results is the validity of a conjecture of J.G. Thompson and
another conjecture of W. Shi and J. Bi for the groups Cn(q),
where n=2m ≥ 4 and q is even.
Download TeX format |
|||||
| back to top | |||||
