Abstract: The author considered the Bousfield equivalence relationship of the stable module category for a finite group, and proved that, if H was a strongly pembedded subgroup of G, then two finitely generated indecomposable kGmodules(kHmodules) were Bousfield equivalent if and only if their Green correspondents were Bousfield equivalent, in addition, Green correspondence induced a onetoone correspondence between Bousfield equivalence classes of Stmod(kG) and those of Stmod(kH).

Key words: stable module category, strongly p-embedded subgroup, Bousfield class, Bousfield equivalence