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Subgroup series
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==Comparison of series== A ''refinement'' of a series is another series containing each of the terms of the original series. Two subnormal series are said to be ''equivalent'' or ''isomorphic'' if there is a [[bijection]] between the sets of their factor groups such that the corresponding factor groups are [[group isomorphism|isomorphic]]. Refinement gives a [[partial order]] on series, up to equivalence, and they form a [[Lattice (order)|lattice]], while subnormal series and normal series form sublattices. The existence of the supremum of two subnormal series is the [[Schreier refinement theorem]]. Of particular interest are ''maximal'' series without repetition.
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