A5

Part of 2016 Putnam

Problems(1)

Source:

G

is a finite group generated by the two elements

g

h,

where the order of

g

is odd. Show that every element of

G

can be written in the form

g^{m_1}h^{n_1}g^{m_2}h^{n_2}\cdots g^{m_r}h^{n_r}

1\le r\le |G|

m_n,n_1,m_2,n_2,\dots,m_r,n_r\in\{1,-1\}.

|G|

is the number of elements of

G.

PutnamPutnam 2016Putnam algebra