Timeline for Prime divisor of finite group

7 events

when toggle format	what		by	license	comment
Dec 4, 2012 at 13:15	vote	accept	Mart
Dec 3, 2012 at 20:49	answer	added	Arturo Magidin		timeline score: 3
Dec 3, 2012 at 19:49	comment	added	Arturo Magidin		@user123: (i) You have failed to clarify what you mean with yoru ntoation. (ii) Take the direct product of the Klein 4-group and a group of order not divisible by 6. You still get exactly 3 elements of order 2, but no elements of order 3.
Dec 3, 2012 at 19:39	comment	added	Mart		@Arturo Magidin: Thanks. Note that $G$ is not $p$-group.
Dec 3, 2012 at 18:54	comment	added	Arturo Magidin		If you are adding the order of all conjugacy classes, then you get the order of $G$, so the result follows from Cauchy's Theorem. If you are only adding conjugacy classes corresponding to elements of a given order, then the answer is no: for the Klein $4$-group, $G$ has 3 elements of order $2$, so $3$ divides the sum of sizes of conjugacy classes of elements of order $2$, but $G$ has no elements of order $3$.
Dec 3, 2012 at 18:31	comment	added	labirintas		What do you sum over in the last sum? Over all the conjugacy classes?
Dec 3, 2012 at 18:16	history	asked	Mart	CC BY-SA 3.0