document: Recognition of finite simple groups S/sub 4 / -LRB- q -RRB- by their element orders It is proved that among simple groups S/sub 4 / -LRB- q -RRB- in the class of finite-groups , only the groups S/sub 4 / -LRB- 3/sup n / -RRB- , where n is an odd number greater than unity , are recognizable by a set of their element orders . It is also shown that simple groups U/sub 3 / -LRB- 9 -RRB- , / sup 3/D/sub 4 / -LRB- 2 -RRB- , G/sub 2 / -LRB- 4 -RRB- , S/sub 6 / -LRB- 3 -RRB- , F/sub 4 / -LRB- 2 -RRB- , and / sup 2/E/sub 6 / -LRB- 2 -RRB- are recognizable , but L/sub 3 / -LRB- 3 -RRB- is not
doc_bio_tags: O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: element orders
abstractive_keyphrases: finite simple groups recognition divisibility relation