MathDB

B6

Part of 1977 Putnam

Problems(1)

Putnam 1977 B6

Source:

4/7/2022
Let HH be a subgroup with hh elements in a group G.G. Suppose that GG has an element aa such that for all xx in H,H, (xa)3=1,(xa)^3=1, the identity. In GG, let PP be the subset of all products x1ax2a…xna,x_1ax_2a\dots x_na, with nn a positive integer and the xix_i in H.H.
(a) Show that PP is a finite set. (b) Show that, in fact, PP has no more that 3h23h^2 elements.
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