TY - JOUR ID - 962 TI - Frattini supplements and Frat- series JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Aydın, Y. AU - Pancar, A. AD - Faculty of Arts and Sciences‎, ‎Department of Mathematics‎, ‎Ondokuz Mayis University‎, ‎Samsun‎, ‎Turkey. Y1 - 2017 PY - 2017 VL - 43 IS - 3 SP - 747 EP - 753 KW - Frattini subgroup‎ KW - ‎primitive group‎ KW - ‎group actions‎ DO - N2 - ‎In this study‎, ‎Frattini supplement subgroup and Frattini supplemented group‎ ‎are defined by Frattini subgroup‎. ‎By these definitions‎, ‎it's shown that‎ ‎finite abelian groups are Frattini supplemented and every conjugate of a‎ ‎Frattini supplement of a subgroup is also a Frattini supplement‎. ‎A group action‎ ‎of a group is defined over the set of Frattini supplements of a normal‎ ‎subgroup of the group by conjugation and in this study new characterization‎ ‎of primitivity of groups has obtained in terms of Frattini supplemented‎ ‎groups by this action‎. ‎Moreover, Frat-series of a group is defined based on‎ ‎Frattini supplements of normal subgroups of the group and it is shown that‎ ‎subgroups and factor groups of groups with Frat-series also have Frat-series‎ ‎under some special conditions‎. ‎Furthermore‎, ‎we determined a characterization of soluble groups which have Frat-series. UR - http://bims.iranjournals.ir/article_962.html L1 - http://bims.iranjournals.ir/article_962_408ef6dcf6b085e43a37f5b92e2f4595.pdf ER -