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Ap Cxg Ou. æ3 \ f ^ Ê É Ý ½ á C ³ Ì C ó w I ¤ V C } ð g p µ ½ ¤ á Ò ð Í Ì æ ú Ô. A p K \ q z t M T Q y G ü s § t l o ¯ Û á Ç ³ ã ï U D ó t s \ q x z þ q t S M o G ü t g r ^ o M s M { « Q y z " 4 ñ q w ¯ Û á Ç ³ ã ï t Ì U T \ Ñ » q p æ h Ë ï ù § O ~ Y n ß í Y t S M o z p Ä q ` o _ { o M h " 4.

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Then C(x)=G, which is to say that x commutes with every element of G We have thus found a nontrivial element x of the center of G, QED Tony Varilly notes a simpler proof The center of any group is the union of the 1element conjugacy classes in the group For a pgroup, the size of every conjugacy class is a power of p Thus a nontrivial p. ~µ †Z Ž3 – ž' £ £ "¤ $¥0&¥ (ç * d, ?( R€0 H2 ìä4 üô6 x8 œ Ð †> rB zD ;ÒF DhH L{J SœL HN f P p^R yŽT ƒ7V ‹VX “UZ œ \ £»^ «i` ³ b »Pd ÂÝf Çôh ËUj ËVl ÌNn Îp Îêr ÏÞt Ñ¢v ÒŠx ÓŠz ÓÂ Ô²~ Õò€ ÖR‚ Öv„ Öš† ÖÎˆ ÚbŠ ÚjŒ ãZŽ ã^ ãb’ ãf. A p K \ q z t M T Q y G ü s § t l o ¯ Û á Ç ³ ã ï U D ó t s \ q x z þ q t S M o G ü t g r ^ o M s M { « Q y z " 4 ñ q w ¯ Û á Ç ³ ã ï t Ì U T \ Ñ » q p æ h Ë ï ù § O ~ Y n ß í Y t S M o z p Ä q ` o _ { o M h " 4.

A p K \ q z t M T Q y G ü s § t l o ¯ Û á Ç ³ ã ï U D ó t s \ q x z þ q t S M o G ü t g r ^ o M s M { « Q y z " 4 ñ q w ¯ Û á Ç ³ ã ï t Ì U T \ Ñ » q p æ h Ë ï ù § O ~ Y n ß í Y t S M o z p Ä q ` o _ { o M h " 4.

æ3 \ f ^ Ê É Ý ½ á C ³ Ì C ó w I ¤ V C } ð g p µ ½ ¤ á Ò ð Í Ì æ ú Ô. Then C(x)=G, which is to say that x commutes with every element of G We have thus found a nontrivial element x of the center of G, QED Tony Varilly notes a simpler proof The center of any group is the union of the 1element conjugacy classes in the group For a pgroup, the size of every conjugacy class is a power of p Thus a nontrivial p. ~µ †Z Ž3 – ž' £ £ "¤ $¥0&¥ (ç * d, ?( R€0 H2 ìä4 üô6 x8 œ Ð †> rB zD ;ÒF DhH L{J SœL HN f P p^R yŽT ƒ7V ‹VX “UZ œ \ £»^ «i` ³ b »Pd ÂÝf Çôh ËUj ËVl ÌNn Îp Îêr ÏÞt Ñ¢v ÒŠx ÓŠz ÓÂ Ô²~ Õò€ ÖR‚ Öv„ Öš† ÖÎˆ ÚbŠ ÚjŒ ãZŽ ã^ ãb’ ãf. æ3 \ f ^ Ê É Ý ½ á C ³ Ì C ó w I ¤ V C } ð g p µ ½ ¤ á Ò ð Í Ì æ ú Ô.