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Minimal Non-nilpotent and Locally Nilpotent Fusion Systems
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作者 Jun Liao Yanjun Liu 《Algebra Colloquium》 SCIE CSCD 2016年第3期455-462,共8页
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
关键词 saturated fusion system minimal non-nilpotent locally nilpotent p-con-strained
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On Local Nilpotency of the Normal Subgroups of a Group
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作者 Zhirang Zhang Jiachao Li 《Algebra Colloquium》 SCIE CSCD 2016年第3期531-540,共10页
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
关键词 normal subgroups nilpotent groups locally nilpotent groups Frattini sub-group Hirsch-Plotkin radical
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Groups with Cyclic Outer Automizers
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作者 Maria Rosaria Celentani Giovanni Cutolo Antonella Leone 《Algebra Colloquium》 SCIE CSCD 2014年第3期381-398,共18页
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.
关键词 automizers locally nilpotent supersoluble soluble groups
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