On the Cayley Isomorphism Problem for Cayley Objects of Nilpotent Groups of Some Orders
Keyword(s):
We give a necessary condition to reduce the Cayley isomorphism problem for Cayley objects of a nilpotent or abelian group $G$ whose order satisfies certain arithmetic properties to the Cayley isomorphism problem of Cayley objects of the Sylow subgroups of $G$ in the case of nilpotent groups, and in the case of abelian groups to certain natural subgroups. As an application of this result, we show that ${\mathbb Z}_q\times{\mathbb Z}_p^2\times{\mathbb Z}_m$ is a CI-group with respect to digraphs, where $q$ and $p$ are primes with $p^2 < q$ and $m$ is a square-free integer satisfying certain arithmetic conditions (but there are no other restrictions on $q$ and $p$).
2002 ◽
Vol 72
(2)
◽
pp. 173-180
◽
Keyword(s):
1998 ◽
Vol 58
(3)
◽
pp. 479-493
◽
Keyword(s):
1995 ◽
Vol 44
(2)
◽
pp. 395-402
◽
Keyword(s):
2011 ◽
Vol 10
(03)
◽
pp. 377-389
Keyword(s):
2017 ◽
Vol 16
(10)
◽
pp. 1750200
◽