Abstract
Group Classes
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.
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© 2009 Springer-Verlag London
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Wehrfritz, B.A.F. (2009). The Basic Theory of Polycyclic Groups. In: Group and Ring Theoretic Properties of Polycyclic Groups. Algebra and Applications, vol 10. Springer, London. https://doi.org/10.1007/978-1-84882-941-1_2
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DOI: https://doi.org/10.1007/978-1-84882-941-1_2
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