Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some result...Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some results about the X-s-permutable subgroups and use them to determine the structure of some finite groups.展开更多
In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble gro...In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.展开更多
基金Foundation item： the National Natural Science Foundation of China （No. 10771180） the Postgraduate Innovation Grant of Jiangsu Province and the International Joint Research Fund between NSFC and RFBR.
文摘Let X be a nonempty subset of a group G. A subgroup H of G is said to be X-spermutable in G if, for every Sylow subgroup T of G, there exists an element x E X such that HT^x= T^xH. In this paper, we obtain some results about the X-s-permutable subgroups and use them to determine the structure of some finite groups.
文摘In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.
