In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgr...In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgroups H of P such that |H| = pdand explore p-supersolvability of G by the conditions of weakly M-supplemented properties of H and psupersolvability of the normalizer NG(H), where 1 ≤ pd<|P |. Also, we study the p-nilpotency of G under the assumptions that NG(P) is p-nilpotent and the weakly M-supplemented condition on a subgroup K such that K_(p)■K and P′≤ K_(p) ≤ Φ(P), Kp is a Sylow p-subgroup K. To some extent, our main results can be regarded as generalizations of the Frobenius theorem.展开更多
Let G be a finite group and F a saturated formation of finite groups.Then G is a quasi-F-group if for every F-eccentric chief factor H/K of G and every x∈G,x induces an inner automorphism on H/K.In this article,we ob...Let G be a finite group and F a saturated formation of finite groups.Then G is a quasi-F-group if for every F-eccentric chief factor H/K of G and every x∈G,x induces an inner automorphism on H/K.In this article,we obtain some results about the quasi-F-groups and use them to give the conditions under which a group is quasisupersoluble.展开更多
A subgroup H of G is called M-supplemented in G if there exists a subgroup B of G such that G = HB and HiB < G for every maximal subgroup Hi of H. In this paper, we use M-suppiemented subgroups to study the structu...A subgroup H of G is called M-supplemented in G if there exists a subgroup B of G such that G = HB and HiB < G for every maximal subgroup Hi of H. In this paper, we use M-suppiemented subgroups to study the structure of finite groups and obtain some new characterization about solvability and p-supersolvability for a fixed prime p. Some results in the literature are corollaries of our theorems.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12001436)the Natural Science Foundation of Sichuan Province(Grant No.2022NSFSC1843)+3 种基金Chunhui Plan Cooperative Scientific Research Project of Ministry of Education of the People’s Republic of Chinathe Fundamental Research Funds of China West Normal University(Grant Nos.17E09118B032)。
文摘In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgroups H of P such that |H| = pdand explore p-supersolvability of G by the conditions of weakly M-supplemented properties of H and psupersolvability of the normalizer NG(H), where 1 ≤ pd<|P |. Also, we study the p-nilpotency of G under the assumptions that NG(P) is p-nilpotent and the weakly M-supplemented condition on a subgroup K such that K_(p)■K and P′≤ K_(p) ≤ Φ(P), Kp is a Sylow p-subgroup K. To some extent, our main results can be regarded as generalizations of the Frobenius theorem.
基金supported by the grant of NSFC(Grant#11701223,11271016,11501235)the Key Natural Science Foundation of Anhui Education Commission(KJ2017A569)Research project of China West Normal University(17E091).
文摘Let G be a finite group and F a saturated formation of finite groups.Then G is a quasi-F-group if for every F-eccentric chief factor H/K of G and every x∈G,x induces an inner automorphism on H/K.In this article,we obtain some results about the quasi-F-groups and use them to give the conditions under which a group is quasisupersoluble.
基金Supported by the NSFC (Grants No. 11871062, 11701223 and 11501235)Natural Science Foundation of Jiangsu Province (Grant No. BK20181451)+1 种基金Key Natural Science Foundation of Anhui Education Commission (Grant No. KJ2017A569)Fundamentai Research Funds of China West Normal University (Grants No. 17E091 and 18B032).
文摘A subgroup H of G is called M-supplemented in G if there exists a subgroup B of G such that G = HB and HiB < G for every maximal subgroup Hi of H. In this paper, we use M-suppiemented subgroups to study the structure of finite groups and obtain some new characterization about solvability and p-supersolvability for a fixed prime p. Some results in the literature are corollaries of our theorems.
