Subgroups of finitely presented groups
1961 ◽
Vol 262
(1311)
◽
pp. 455-475
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Keyword(s):
The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It follows that every countable A belian group, and every countable locally finite group can be so embedded; and that there exists a finitely presented group which simultaneously embeds all finitely presented groups. A nother corollary of the theorem is the known fact that there exist finitely presented groups with recursively insoluble word problem . A by-product of the proof is a genetic characterization of the recursively enumerable subsets of a suitable effectively enumerable set.
1973 ◽
Vol 8
(1)
◽
pp. 27-60
◽
1974 ◽
Vol 18
(1)
◽
pp. 1-7
◽
2009 ◽
Vol 02
(04)
◽
pp. 611-635
◽
2018 ◽
Vol 28
(07)
◽
pp. 1299-1381
1992 ◽
Vol 53
(3)
◽
pp. 369-376
◽
2004 ◽
Vol 70
(2)
◽
pp. 199-205
◽
1998 ◽
Vol 1
◽
pp. 25-41
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Keyword(s):