A note on the Jordan-Hölder theorem (Q1115968)

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.\}