On HNN-extensions in the class of groups of large odd exponent
| dc.creator | Ivanov, S. V. | |
| dc.date | 2002-10-13 | |
| dc.date.accessioned | 2026-07-07T04:51:53Z | |
| dc.date.available | 2026-07-07T04:51:53Z | |
| dc.description | A sufficient condition for the existence of HNN-extensions in the class of groups of odd exponent $n \gg 1$ is given in the following form. Let $Q$ be a group of odd exponent $n > 2^{48}$ and $\mathcal G$ be an HNN-extension of $Q$. If $A \in \mathcal G$ then let $\mathcal F(A)$ denote the maximal subgroup of $Q$ which is normalized by $A$. By $τ_A$ denote the automorphism of $\mathcal F(A)$ which is induced by conjugation by $A$. Suppose that for every $A \in \mathcal G$, which is not conjugate to an element of $Q$, the group $<τ_A, \mathcal F(A)>$ has exponent $n$ and, in addition, equalities $A^{-k} q_0 A^{k} = q_k$, where $q_k \in Q$ and $k =0, 1, ..., [2^{-16}n]$ ($[2^{-16}n]$ is the integer part of $2^{-16}n$), imply that $q_0 \in \mathcal F(A)$. Then the group $Q$ naturally embeds in the quotient $\mathcal G / \mathcal G^n$, that is, there exists an analog of the HNN-extension $\mathcal G$ of $Q$ in the class of groups of exponent $n$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0210190 | |
| dc.identifier | http://arxiv.org/abs/math/0210190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65269 | |
| dc.subject | Group Theory | |
| dc.subject | Primary 20E06, 20F50; Secondary 20F05, 20F06 | |
| dc.title | On HNN-extensions in the class of groups of large odd exponent | |
| dc.type | text |