Abstract
Two sufficient conditions for a finite group G to be p-supersolvable have been obtained. For example (Theorem 1.1), let N be a normal subgroup of G such that G/N is p-supersolvable for a fixed odd prime p and let N p be a Sylow p-subgroup of N. Suppose that N is p-solvable and Ω1(N p) is generated by the subgroups of order p of N p which are normal in N G(N p). Then G is p-supersolvable.
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This research is supported by Natural Science Foundation of China and NSF of Shanxi Province (No. 20051007) and Returned Oversea Students Foundation of Shanxi Province (No. Jinliuguanban [2004] 7).
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Li, R.S., Zhang, Q.H. A note on p-supersolvable groups. Acta Math Hung 116, 27–34 (2007). https://doi.org/10.1007/s10474-007-5267-7
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DOI: https://doi.org/10.1007/s10474-007-5267-7