A composition series is a way of describing a group.
The quotient groups are called the quotients of the series. We call a composition series finer than a composition series if the terms of are taken from the terms of . Note, however, that in general, a composition series with some terms omitted is no longer a composition series, since in general if is a normal subgroup of and is a normal subgroup of , then is not necessarily a normal subgroup of .
Two composition series and (of not necessarily identical groups and ) are considered equivalent if , and there is a permutation of the integers in such that and are isomorphic for all integers .
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