TY - JOUR
ID - 110821
TI - n-capability of A-groups
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Chakaneh, Marzieh
AU - Kayvanfar, Saeed
AU - Hatamian, Rasoul
AD - Department of Pure Mathematics,
Ferdowsi University of Mashhad,
P. O. Box 1159, Mashhad 91775, I. R. Iran
AD - Department of Pure Mathematics,
Payame Noor University,
Tehran, I. R. Iran
Y1 - 2020
PY - 2020
VL - 5
IS - 4
SP - 345
EP - 353
KW - n-Capable group
KW - Sylow subgroup
KW - Frattini subgroup
DO - 10.22052/mir.2020.240334.1251
N2 - Following P. Hall a soluble group whose Sylow subgroups are all abelian is called A-group. The purpose of this article is to give a new and shorter proof for a criterion on the capability of A-groups of order p2q, where p and q are distinct primes. Subsequently we give a sufficient condition for n-capability of groups having the property that their center and derived subgroups have trivial intersection, like the groups with trivial Frattini subgroup and A-groups. An interesting necessary and sufficient condition for capability of the A-groups of square free order will be also given.
UR - https://mir.kashanu.ac.ir/article_110821.html
L1 - https://mir.kashanu.ac.ir/article_110821_0abe1545736a161f9fd287d64f272d75.pdf
ER -