During this time he proved Zassenhaus's lemma, a beautiful result on subgroups which can be used to give a simple proof of the Jordan - Hölder theorem.

Please remove spaces between words.
DuringthistimeheprovedZassenhaus'slemma,abeautifulresultonsubgroupswhichcanbeusedtogiveasimpleproofoftheJordan-Höldertheorem.