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You are not logged in. #1 20121128 03:57:55
grouplet G be a group of order p^2 where p is a prime no. let x belongs to G. prove that {y belongs to G: xy=yx}=G #3 20121129 01:03:04
Re: groupHi The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20121129 03:06:40
Re: groupWhat operation are you using in "xy=yx"? Last edited by anonimnystefy (20121129 03:19:56) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20121129 19:47:37
Re: groupI'm wondering if the following is any help. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #9 20121130 00:43:45
Re: groupHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20121130 03:35:19
Re: groupBy base element, I'm assuming you mean x. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #11 20121130 23:42:00
Re: groupIt is a wellknown result that every pgroup has a nontrivial centre. (This can be proved by counting conjugacy classes.) Hence if , p prime, either or by Lagrange. Suppose . Then and so is cyclic, say . Let . Then and for some integers . Thus and for some . Hence x and y commute. Thus G is Abelian and so . (Thus the case is acutally impossible.) #12 20121201 00:35:23
Re: groupArgh! I've just realized that the subgroup princess snowwhite is defining is not the centre of G but the centralizer of a fixed element x in G: . (This is a subgroup of G). However, note that is a subgroup of . Hence if (as I proved above) then necessarily as well – so no harm done. 