Universal group with twenty-one defining relations

✍ Scribed by M.K. Valiev

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 416 KB
• Volume: 17
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(77)90153-4

✦ Synopsis

11 is proved that every finit,.ly presented group .':.an be embedded in a group with twenty-one defining relations.

The immediate consequence of the well-known theorem of Higman is that there exist universal finitely presented (f.p.) groups, i.e. groups in which every f.p. group (and consequently every recursively presented group) can be embedded. In we have presented generators and defining relations for one such group (this gro,.~p U, has forty-two defining relations) and remarked that there exists a universal group U2 with twenty-seven defining relations (earlier in we have announced somewhat weaker. ~ Jults ~. Some later in [2) Boone and Collins proved that every f.p. group can be embedded in a group with twenty-six defining relation:; In their proof a modification i:~ used of the proof of the Higman's theorem b,, Aanderaa . The Aanderaa's proof is rather dose to our proof in [8], however it i~; obtained independently and differs from our proof in essential details. In this pape" we shall prove the following assertion.