The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal...The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent （resp., locally p-nilpotent） groups.展开更多
A group G is said to have property μ whenever N is a non-locally nitpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property v satisfy property μ, where a grou...A group G is said to have property μ whenever N is a non-locally nitpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property v satisfy property μ, where a group G is said to have property v if every non-nilpotent normal subgroup of G has a finite non-nilpotent G-quotient. HP（G） is the Hirsch-Plotkin radical of G, and φf （G） is the intersection of all the maximal subgroups of finite index in G （here φf（G） = G if no such maximal subgroups exist）. It is shown that a group G has property μ if and only if HP（G/φf（G）） = HP（G）/φf（G） and that the class of groups with property v is a proper subclass of that of groups with property it. Also, the structure of the normal subgroups of a group： nilpotency with the minimal condition, is investigated.展开更多
We consider groups G such that NG（H）/HCG（H） is cyclic for all H ≤ G. More specifically, we characterise locally nilpotent and supersoluble groups with this property.
基金Supported by the National 973 Project （452101650122） and the National Natural Science Foundation of China （11201194, 11301393）. In addition, the second author was supported by the doctoral foundation of Jiangxi Normal University.
文摘The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent （resp., locally p-nilpotent） groups.
基金Project supported by the National Natural Science Foundation of China （Nos. 11371335, 11471055）.
文摘A group G is said to have property μ whenever N is a non-locally nitpotent normal subgroup of G, there is a finite non-nilpotent G-quotient of N. FC-groups and groups with property v satisfy property μ, where a group G is said to have property v if every non-nilpotent normal subgroup of G has a finite non-nilpotent G-quotient. HP（G） is the Hirsch-Plotkin radical of G, and φf （G） is the intersection of all the maximal subgroups of finite index in G （here φf（G） = G if no such maximal subgroups exist）. It is shown that a group G has property μ if and only if HP（G/φf（G）） = HP（G）/φf（G） and that the class of groups with property v is a proper subclass of that of groups with property it. Also, the structure of the normal subgroups of a group： nilpotency with the minimal condition, is investigated.
文摘We consider groups G such that NG（H）/HCG（H） is cyclic for all H ≤ G. More specifically, we characterise locally nilpotent and supersoluble groups with this property.
