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A note on the Jordan-Hölder theorem. (English) Zbl 0665.20011
The object of this note is to prove Jordan-Hölder type results such as the following Theorem 3.3: Given two chief series of the finite group G and a subgroup P which covers or avoids every chief factor of G, there is a 1-1 correspondence between chief factors in these series covered by P such that corresponding chief factors have the same order (but are not necessarily G-isomorphic).
{Reviewer’s Remark: Using an argument as in the proof of 3.2 of the reviewer’s [Commun. Algebra 16, 1627-1638 (1988; Zbl 0649.20020)], one can actually show that there is a 1-1 correspondence between the chief factors in these series such that two corresponding factors are both covered or both avoided by P and, moreover, are P-isomorphic.}
Reviewer: P.Förster

MSC:
20D30 Series and lattices of subgroups
20F14 Derived series, central series, and generalizations for groups
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References:
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