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有限群共轭类长的一个问题
On a Problem of the Length of Conjugacy Classes of Finite Groups
设A和B都是有限群G的子群且G=AB.若A是G的次正规子群，且对每个p∈π（G）以及每个素数幂阶的p'-元x∈A∪B，p2均不整除|xG|，则G为超可解群.这个结果正面解答了由石向东，韦华全和马儇龙于2013年提出的一个问题，统一推广了由刘晓蕾于2011年得到的三个定理.
Let G be a finite group with subgroups A and B such that G=AB. If A is subnormal in G and for any p∈π(G) and any p'-element x of A∪B with prime power order,|xG| is not divisible by p2, then G is supersolvable. This result gives a positive answer to a problem posed in 2013 by Shi Xiangdong, Wei Huaquan and Ma Xuanlong and a unify generalization of three theorems obtained in 2011 by Liu Xiaolei.
有限群 / 可解群 / 超可解群 / 共轭类长 / 次正规子群 {{custom_keyword}} /
finite group / solvable / supersolvable / length of conjugacy class / subnormal {{custom_keyword}} /
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国家自然科学基金资助项目（11361006，11161006）；广西大学科研基金资助项目（XGZ130761）
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