Free groups and free products

Reference no: EM13117992

a. Show that in the free product, the center Z (G_1 x G_2) is trivial if |G_1| > 1 and |G_2| > 1.

b. Determine the elements of finite order in G_1 x G_2.

c. Show that the free group on a set X has no elements of finite order ( other than the identity).

Reference no: EM13117992

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