I would like to proof the following in the case of groups of finite order: the number of elements of an arbitrary class of conjugated elements is a divider of the index (G:Z) of the centre of G. Does anybody know how to proof this? Peter Mulder
Follow Math Help Forum on Facebook and Google+
Originally Posted by PeterMulder I would like to proof the following in the case of groups of finite order: the number of elements of an arbitrary class of conjugated elements is a divider of the index (G:Z) of the centre of G. Does anybody know how to proof this? Peter Mulder Let a group act on itself by conjugation: , then , with the centralizer of in Since is the equivalence class of and since , we're done by Lagrange's theorem Tonio
Thank you Tonio!
View Tag Cloud