Subgroups of Finite Index in Free Groups
- 1 April 1949
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 1 (2) , 187-190
- https://doi.org/10.4153/cjm-1949-017-2
Abstract
This paper has as its chief aim the establishment of two formulae associated with subgroups of finite index in free groups. The first of these (Theorem 3.1) gives an expression for the total length of the free generators of a subgroup U of the free group Fr with r generators. The second (Theorem 5.2) gives a recursion formula for calculating the number of distinct subgroups of index n in Fr.Of some independent interest are two theorems used which do not involve any finiteness conditions. These are concerned with ways of determining a subgroup U of F.Keywords
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