A Bowen type rigidity theorem for non-cocompact hyperbolic by Xiangdong Xie

By Xiangdong Xie

We identify a Bowen kind pressure theorem for the basic staff of a noncompacthyperbolic manifold of finite quantity (with measurement no less than 3).

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Extra resources for A Bowen type rigidity theorem for non-cocompact hyperbolic groups

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LeT). Suppose that HI c c H n = A is a series of normal subgroups ofG. Assume that, for i = 1, , n, there is no normal subgroup N of G such that H i - l c Ne Hi' If gE S-T and [Hi' g, g] ~ H i - l for i = 1, ... 2. 2. C Proof By the definition of a chief factor, Hj Hi _ 1 is a chief factor of G for i = I, ... , n. Suppose CCT) ~ T. Let K be th(l set of all x E G such that [Hi' x] ~ H i - l for i = 1, ... , n. By Lemma lOA, K

The analogue to Goldschmidt's Theorem is false if p is odd. Let q = p(p-l) and let H = SL(2, 2 Q). Then H is a simple group with a cyclic Sylow psubgroup. By elementary number theory, p2. IHlp ; : : Let A be a cyclic group of order p. Consider G to be a trivial operator group on A. Let N = N(Kao(S». 4 is equivalent to a statement about cohomology groups (Hall, 1959) namely, H 1(G, A) ~ H 1(N, A) if p ;;::: 5. 1) This suggests the following problem related to Professor Alperin's lecture. 8. Does there exist a function f from the positive integers to the positive integers such that Hi(G, A) ~ Hi(N, A) Appendix Al.

1, Gorenstein, 1968). However, we may give a short direct proof. Let N be a subgroup of maximal order in M subject to the condition that N = N l X N 2 X ••. x N r for some r ~ I and some minimal normal subgroups N l , Nb' .. , N r of H. For any Ni and any 9 E G, (Nj )9 is a minimal normal subgroup of H because H

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