S.O.S. Mathematics CyberBoard

Trying to understand normal subgroups . Book says H is a normal subgroup if, for a in H and x in G, xax^-1 is in H.

Does this mean for example say i have a groups under the operation of multiplication: G={e,1,2,1/2,3,1/3} and H is a subgroup of G, ie H={e, 2, 1/2}

then H is normal since for example 3x2x(1/3)=2 and 1x2x2=2, 2 is in H ?

Is G a group? Isn't ?

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The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low, and achieving our mark. - Michelangelo Buonarroti

yea you are right. change it to G={0,1,2,1/2} H={2,1/2}

Or give me an example