Talk:Lagrange's theorem (group theory)

Historical note
"Lagrange did not prove his theorem; all he did, essentially, was to discuss some special cases." This was for a very good reason: the notion of a group did not exist in Lagrange's day. It was invented by Galois several decades later. Apparently Lagrange's argument was applicable to groups once they were formulated, so he was given credit for the general theorem. CharlesTheBold (talk) 13:11, 13 March 2013 (UTC)

Inversion
"Sylow's theorem extends this to the existence of a subgroup of order equal to the maximal power of any prime dividing the group order."

Really, Sylow's theorem say about any power of prime, not necessarily maximal. 95.104.210.134 (talk) —Preceding undated comment added 12:11, 13 April 2013 (UTC)

'Proof' Section
This section doesn't appear to contain a valid proof, and thus should perhaps be changed to something like 'Outline of Proof...'

This first paragraph says "If we can show that all cosets of H have the same number of elements..." (the theorem would follow), but it doesn't show that the cosets do in fact have the same number of elements, and so the result is not proved, absent more detail not given in the article. — Preceding unsigned comment added by ChengduTeacher (talk • contribs) 13:38, 24 October 2014 (UTC)

First Paragraph
Entirely an amateur here, but isn't the 'number of elements' of a group better referred to as its 'cardinality'? 'Order' already seems to be used in more than one way. It would also allow insertion of a reference to 'Cardinality', and introduce the |H| notation. It also appears that the index is more commonly |G:H| (not [G:H]), see. Captain Puget (talk) 23:40, 11 January 2021 (UTC)