Journal
ACTA MATHEMATICA HUNGARICA
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1007/s10474-023-01376-w
Keywords
maximal subgroup; invariant subgroup; coprime action; c-normality; solvability criterion; p-nilpotency
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This paper studies c-normality in the coprime action setting and obtains several solvability and p-nilpotency criteria in terms of certain subsets of maximal invariant subgroups of a group or of its Sylow subgroups.
A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G such that G = HN and H boolean AND N <= coreG(H), the largest normal subgroup of G contained in H. c-Normality is a weaker form of normality, introduced by Y.M. Wang, that has led to interesting results and structural criteria of finite groups. In this paper we study c-normality in the coprime action setting so as to obtain several solvability and p-nilpotency criteria in terms of certain subsets of maximal invariant subgroups of a group or of its Sylow subgroups.
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