Abstract
The essentials of group theory can be summarized in few mathematical definitions that admit a description in relatively simple words.
Ancora indietro un poco ti rivolvi,
diss’io, là dove di’ ch’usura offende
la divina bontade, e ’l groppo solvi.
Dante, Inferno XI, 94
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Notes
- 1.
[Cayley’s footnote]: The idea of a group as applied to permutations or substitutions is due to Galois, and the introduction of it may be considered as marking an epoch in the progress of the theory of algebraic equations.
- 2.
Following a convention widely utilized in finite group theory we make a distinction between subgroups and normal subgroups. The notation \(G \supset H\) simply means that H is a subgroup of G, not necessarily an invariant one. On the other hand \(G\vartriangleright N\) means that N is a normal (invariant) subgroup of G.
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Fré, P.G. (2018). How Group Theory Came into Being. In: A Conceptual History of Space and Symmetry . Springer, Cham. https://doi.org/10.1007/978-3-319-98023-2_3
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DOI: https://doi.org/10.1007/978-3-319-98023-2_3
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