The solution of length three equations over groups
1983 ◽
Vol 26
(1)
◽
pp. 89-96
◽
Keyword(s):
Let G be a group, and let r = r(t) be an element of the free product G * 〈G〉 of G with the infinite cyclic group generated by t. We say that the equation r(t) = 1 has a solution in G if the identity map on G extends to a homomorphism from G * 〈G〉 to G with r in its kernel. We say that r(t) = 1 has a solution over G if G can be embedded in a group H such that r(t) = 1 has a solution in H. This property is equivalent to the canonical map from G to 〈G, t|r〉 (the quotient of G * 〈G〉 by the normal closure of r) being injective.
1969 ◽
Vol 10
(1-2)
◽
pp. 162-168
◽
Keyword(s):
1953 ◽
Vol 49
(4)
◽
pp. 579-589
◽
Keyword(s):
1971 ◽
Vol 23
(1)
◽
pp. 69-76
◽
Keyword(s):
Keyword(s):
Keyword(s):