Theoretical analysis demonstrates Frattini subgroup embeddings in infinite nilpotent groups, highlighting structural preservation across finitely generated and Cernikov classes.
In this paper, two Frattini embedding theorems on nilpotent groups are proved. First, let [Formula: see text] be a finitely generated nilpotent group whose torsion subgroup is a finite [Formula: see text]-group, and then there exists a finitely generated nilpotent group [Formula: see text] whose torsion subgroup is also a finite [Formula: see text]-group such that [Formula: see text]. Second, let [Formula: see text] be a nilpotent Cernikov [Formula: see text]-group for a finite set [Formula: see text] of primes, and then there exists a nilpotent Cernikov [Formula: see text]-group [Formula: see text] such that [Formula: see text] and [Formula: see text].
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Zhao et al. (2026) studied this question.
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