MathDB

Putnam 1976 B2

Source:

April 19, 2022

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Problem Statement

Suppose that

G

is a group generated by elements

A

and

B

, that is, every element of

G

can be written as a finite "word"

A^{n_1}B^{n_2}A^{n_3}\dots B^{n_k},

where

n_1,\dots n_k

are any integers, and

A^0=B^0=1

as usual. Also suppose that

A^4=B^7=ABA^{-1}B=1, A^2\neq 1,

and

B\neq 1.

(a) How many elements of

G

are of the form

C^2

with

C

in

G

? (b) Write each such square as a word in

A

and

B.

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