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Welcome to Groupprops, The Group Properties Wiki (beta). 7000+ articles, including most basic group theory material. It is managed by Vipul Naik, a Ph.D. in Mathematics at the University of Chicago. It is part of a broader subject wikis initiative -- see the subject wikis reference guide for more details.
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Basic definitions in group theory, basic facts in group theory, and elementary non-basic facts in group theory pages. There's much much more in the wiki!
Pages on symmetric group:S3 (see also subgroups, elements, representations), symmetric group:S4 (see also subgroups, elements, and representations), dihedral group:D8 (see also subgroups, elements, representations, and endomorphisms/automorphisms),symmetric group:S5 (see also subgroups, elements, and representations), quaternion group (see also subgroups, elements, and representations), alternating group:A4, alternating group:A5, and many more.
Incomplete (not fully finished) guided tour for beginners; the part prepared so far goes over the basic definitions of groups, subgroups, cosets, basic results such as Lagrange's theorem, and a little more, along with stimulating exercises.