The Basic Theory of Polycyclic Groups
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This is effectively just a language, developed by P.Hall in the 1950’s and 60’s to make certain types of group theoretic arguments more concise while highlighting the essential components of the proof.
A group class is a class X of groups such that H ≅ G∈X implies H∈X (the main condition; effectively we are dealing with isomorphism classes of groups rather than the groups themselves) and such that 〈1〉∈X (a convenient convention). For certain commonly used classes we have special notations. These include the following.
KeywordsNormal Subgroup Basic Theory Isomorphism Class Nilpotent Group Closure Operator
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