I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 3, PAGES 675-683
On the groups in which the subgroups with fixed number of generators
G. N. Arjantseva
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We prove here that, in a definite statistical meaning, in almost
every group with generators and
suppose and to be fixed) all
-generated subgroups of infinite index are free
an arbitrary preassigned bound, possibly ) and all
subgroups of finite index are not free.
To prove this fact we found the condition on relations which guarantee
that all subgroups of infinite index with fixed number of generators
in a finitely presented group are free.
This condition is formulated by means of the finite marked graphs.
All articles are
published in Russian.
Last modified: January 20, 2000