Characterization of finite groups with a unique non-nilpotent proper subgroup
نویسندگان
1 Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, Iran
2 Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, Iran
doi
10.22108/ijgt.2019.116209.1543چکیده
We characterize finite non-nilpotent groups $G$ with a unique non-nilpotent proper subgroup. We show that $|G|$ has at most three prime divisors. When $G$ is supersolvable we find the presentation of $G$ and when $G$ is non-supersolvable we show that either $G$ is a direct product of an Schmidt group and a cyclic group or a semi direct product of a $p$-group by a cyclic group of prime power order.
