1 answer

0 Let (f.) be a group, show that (ly) G where Gly); = Lael | ag=...

Question:

0 Let (f.) be a group, show that (ly) G where Gly); = Lael | ag= ga & gely is the center of G. (So, show that cly)< ; & cgjat

0 Let (f.) be a group, show that (ly) G where Gly); = Lael | ag= ga & gely is the center of G. (So, show that cly)< ; & cgjat. ) @ let y be a group, gel & Haf. Prove that Ks4 where us Ki Cig) := {acly I ag = gay is the centralizer of g inily, and K: N (H): = hatly I aH=Hay in the normalizen of Henly.

Answers

о 4+ (С.) е едир- to showe; e(g) & g whore ((g) = {at glag=ga let e be the identity on eg 5. = %-e +4 the eccle) liby defa ofФ іри тур 4 4 4 4 н< 4. • К= , (1) { at 41 *1*1 to show, KE G. on eg=ge where e is the identity :. еек .</p><p>K is non empty + bвкNU KE NGCH) = {acg|at= Ha}. where As eH= He e GK e is the identity at ¢ =) K is son empty. ut O. ab ek => bled= Hb =) H6 = 6

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