of a group H, where A and B are isomorphic subgroups of H and φ : A → B is an isomorphism, results from adding to H a new generator t such that the conjugation of the subgroup A ≤ H by t realizes the isomorphism φ. We also say that A and B in (2) are the associated subgroups. One of the first important applications of HNN-extensions was a more transparent proof of the celebrated result of Novik...

To integrate the hierarchy structure of discrimination between all HMM states for Chinese Initials and Finals, we constructed in this paper Hierarchical Neural Networks (HNN), which differ from Jordan's HME in such extensions as more complex parameterization for gate and/or expert and dimension-reduced expert network. With these extensions, we can reuse those pre-trained simple node networks in...

This note includes supporting material for Guilbault’s one-hour talk summarized elsewhere in these proceedings. We supply the group theory necessary to argue that Guilbault’s tame ends cannot be pseudocollared. In particular, we show that certain groups (the interated Baumslag-Solitar groups) cannot have any non-trivial perfect subgroups. The absence of non-trivial perfect subgroups, in turn, e...