Cayley's theorem [SEP] named after
Cayley's theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group "G" is isomorphic to a subgroup of the symmetric group acting on "G". This can be understood as an example of the group action of "G" on the elements of "G".
A permutation of a set "G" is any bijective function taking "G" onto "G". The set of all permutations of "G" forms a group under function
sporadic simple groups.
Main theorems.
Main theorems Lagrange's theorem.
For any finite group "G", the order (number of elements) of every subgroup "H" of "G" divides the order of "G". The theorem is named after Joseph-Louis Lagrange.
Main theorems Sylow theorems.
This provides a partial converse to Lagrange's theorem giving information about how many subgroups of a given order are contained in "G".
Main theorems Cayley's theorem.
Cayley's theorem