On a problem posed by S. Li and J. Liu
A subgroup H of a finite group G is said to be Hall normally embedded in G if there is a normal subgroup N of G such that H is a Hall subgroup of N. The aim of this note is to prove that a group G has a Hall normally embedded subgroup of order |B| for each subgroup B of G if and only if G is soluble with nilpotent residual cyclic of square-free order. This is the answer to a problem posed by Li and Liu (J. Algebra 388:1–9, 2013).
Mathematics Subject Classification (2010)20D10 20D20
KeywordsFinite group Soluble group Hall subgroups
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