摘要
利用完全c-可换子群的概念,得到了幂零群的2个充分条件:(1)如果群G的4阶循环子群在G中完全c-可换且G的任意极小子群含于Z∞(G)中,那么G是幂零群;(2)设N■G且G/N是幂零群.如果N的任意4阶循环子群在G中完全c-可换且N的任意极小子群包含在Z∞(G)中,那么G是幂零群.
Using the concept, completely c- permutable subgroup of finite groups, two sufficient conditions of nilpotent groups was obtained : ( 1 ) If any cyclic subgroup of G of order 4 is completely c - permutable in G and any minimal subgroup of G is contained in the hypercenter ofG , then G is a nilpotent group. ( 2 ) Let N be a normal subgroup ofG and G/N be a nilpotent group. If any cyclic subgroup of N of order 4 is completely c-permutable in G and any minimal subgroup of N is contained in hypercenter ofG , then G is a nilpotent group.
出处
《高师理科学刊》
2008年第6期1-3,共3页
Journal of Science of Teachers'College and University
基金
国家自然科学基金资助项目(10771180)
关键词
有限群
完全c-可换子群
极小子群
幂零群
finite group
C - permutable subgroup
minimal subgroup
nilpotent group