document: Embedding the outer automorphism group Out -LRB- F/sub n / -RRB- of a free group of rank n in the group Out -LRB- F/sub m / -RRB- for m > n It is proved that for every n > or = 1 , the group Out -LRB- F/sub n / -RRB- is embedded in the group Out -LRB- F/sub m / -RRB- with m = 1 + -LRB- n - 1 -RRB- k/sup n / , where k is an arbitrary natural number coprime to n - 1
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 O O O O O O O O O O O O O O O O O B I I I O O O O
extractive_keyphrases: free group arbitrary natural number coprime
abstractive_keyphrases: outer automorphism group embedding