Editing Glossary of group theory (section)

== A ==
{{glossary}}
{{term|1=abelian group}}
{{defn|1=A group {{math|(''G'', •)}} is [[Abelian group|abelian]] if {{math|•}} is commutative, i.e. {{math|1=''g'' • ''h'' = ''h'' • ''g''}} for all {{math|''g'', ''h'' &isin; ''G''}}. Likewise, a group is ''nonabelian'' if this relation fails to hold for any pair {{math|''g'', ''h'' &isin; ''G''}}.}}
{{term|1=ascendant subgroup}}
{{defn|1=A {{gli|subgroup}} {{math|''H''}} of a group {{math|''G''}} is [[ascendant subgroup|ascendant]] if there is an ascending {{gli|subgroup series}} starting from {{math|''H''}} and ending at {{math|''G''}}, such that every term in the series is a {{gli|normal subgroup}} of its successor. The series may be infinite. If the series is finite, then the subgroup is {{gli|subnormal subgroup|subnormal}}.}}
{{term|1=automorphism}}
{{defn|1=An [[group automorphism|automorphism]] of a group is an {{gli|isomorphism}} of the group to itself.}}
{{glossary end}}