Stability automorphism of subnormal series
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This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]
Definition
Symbol-free definition
An automorphism of a group is said to be a stability automorphism with respect to a subnormal series if it induces the identity map on each successive quotient for the subnormal series.
The stability automorphisms of any fixed subnormal series form a group, called the stability group of that subnormal series. This group lives as a subgroup of the automorphism group.
Definition with symbols
An automorphism σ of a group G is termed a stability automorphism with respect to the subnormal series:
if σ(Hix) = Hix for any 
, or equivalently, σ acts as identity on Hi + 1 / Hi.
(An analogous definition can be given for subnormal series indexed by infinite sets).
