|
2 | deleted superfluous "relatively free" | ||
|
Does there exist a variety of groups $\mathfrak{V}$ such that the relatively $\mathfrak{V}$-free group of rank 2 is finite, but the relatively $\mathfrak{V}$-group of rank 3 is infinite? (In other varieties of algebras this can occur; for example, in the variety of all lattices, the free lattice of rank 2 is finite, but the relatively free lattice of rank 3 is infinite.) |
||||
|
|
1 |
|
||
Varieties of groups with infinite relatively free group of rank 2 finite, infinite in rank 3Does there exist a variety of groups $\mathfrak{V}$ such that the relatively $\mathfrak{V}$-free group of rank 2 is finite, but the relatively $\mathfrak{V}$-group of rank 3 is infinite? (In other varieties of algebras this can occur; for example, in the variety of all lattices, the free lattice of rank 2 is finite, but the relatively free lattice of rank 3 is infinite.)
|
||||
