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i've just started out with a course in group theory...here's a question that's been bothering me for a while now...
let G be a group and 'a' ,a unique element of order 2 in G. show that a belongs to Z(G).
if every element of the group has order 2 this is pretty easy....but that's not the case. one thing i've noted is a = a^-1..but does that help?
let G be a group and 'a' ,a unique element of order 2 in G. show that a belongs to Z(G).
if every element of the group has order 2 this is pretty easy....but that's not the case. one thing i've noted is a = a^-1..but does that help?