in this paper, we will give necessary and sufficient conditions for certain hnnextensions of subgroup separable groups with normal associated subgroup to be conjugacyseparable. in fact, we will show that these hnn extensions are conjugacy separable if and onlyif the normalizer of one of its associated subgroup is conjugacy separable.

We construct an example of a torsion free freely indecomposable nitely presented non quasiconvex subgroup H of a word hyperbolic group G such that the limit set of H is not the limit set of a quasiconvex subgroup of G In particular this gives a counterexample to the conjecture of G Swarup that a nitely presented one ended subgroup of a word hyperbolic group is quasiconvex if and only if it has ...

This note shows how to construct a representation of the automorphic extension G of the simple group S = O 8 (5) by a symmetric group on three points, together with an embedding of the normalizer H of an O 8 (2) type subgroup of O + 8 (5). As an application, it is shown that the permutation representation of G on the cosets of H has a base of length two. This question arose in [BGS].

Defending networks against today's attackers is especially challenging for modern intrusion detection/prevention systems for two reasons: the sheer amount of state they must maintain, and the possibility of resource exhaustion attacks on the defense system itself. Our work shows how to cope with these challenges in the context of a TCP stream normalizer whose job is to detect all instances of i...