Talk:Subgroup
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subgroup operation or product
[edit]If in the definition of group one speaks of a generic operation *, why is so that in the definition of subgroup (or rather in the explanations below the definition, at the first property of subgroups) this operation has become a product? Is it language misuse, or is it a requirement?
Put another way: If the set of real numbers R forms a group under the operation +, with identity 0 and inverse -a, is the set of integers Z a subgroup of R under the operation +?
If so: can we speak of operator + as a product? This would be very confusing, although I could admit it as a convenient shortcut. However, in Wikipedia, we may want to guide the unexpert reader a little better.
Joan Solà (talk) —Preceding undated comment added 08:04, 2 June 2016 (UTC)
The giant Cayley tables
[edit]I'm sorry, but I feel that the giant Cayley tables need to be removed. Their inclusion makes what should be an easy task (classifying the subgroups of Z/8Z and S_4) look incredibly complicated. None of the commonly-used algebra textbooks, such as those by Artin, Dummit & Foote, Fraleigh, Lang, etc., explain subgroups by using giant tables like these. Ebony Jackson (talk) 03:34, 21 December 2022 (UTC)