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Subgroups of Finite Index in Free Groups

Published online by Cambridge University Press:  20 November 2018

Marshall Hall Jr.
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 2 , 01 April 1949 , pp. 187 - 190
Copyright
Copyright © Canadian Mathematical Society 1949

References

[1] Hall, M., Jr. and Rado, T., “On Schreier Systems in Free Groups,” Trans. Amer. Math. Soc, vol. 64 (1948), 386–408.Google Scholar
[2] Schreier, O., “Die Untergruppen der freien Gruppen,” Abh. Math. Sent. Hansischen Univ., vol. 5 (1927), 161-183.Google Scholar