Burnside's Problem gave
rise to an enormous body of publications concerning the finiteness
of finitely generated groups of bounded exponents.
Burnside published the first English language
book on the subject of groups. His less-than-prophetic
quote from the preface of The Theory
of Groups of Finite Order (1897) has become famous:
. . it
would be difficult to
find a result
[in pure group theory] that could be most directly obtained by the
consideration of groups of linear transformations."
matter what his initial concerns, he had opened a new field. Over
next 15 - 20 years Burnside and others thrived on his
published 70 mathematical papers while serving as professor of
mathematics at the Royal Naval College at Greenwich, an institution
dedicated to the training of naval officers, not mathematicians.