Can "each" be a subject in a sentense?

Hello,

Suggest please, can the pronoun "each" be a subject of a clause, in

which the real agent, i.e. that whom "each" refers to, is implied? For

instance, can I omit "person" in the following sentence?

"The human desire to lead becomes especially vivid while people
compete in a sport; each [person] tries to jump higher, run faster,...

Thanks in advance.

--

Victor