Difference between revisions of "Dicyclic group"
From Encyclopedia of Mathematics
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| − | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1974) {{ISBN|0-521-20125-X}} {{ZBL|0732.51002}}</TD></TR> |
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Latest revision as of 20:50, 23 November 2023
2020 Mathematics Subject Classification: Primary: 20F05 [MSN][ZBL]
A finite group of order $4n$, obtained as the extension of the cyclic group of order $2$ by a cyclic group of order $2n$. It has the presentation $\langle n,2,2 \rangle$ and group presentation $$ A^n = B^2 = (AB)^2 \ . $$ It may be realised as a subgroup of the unit quaternions.
The dicyclic group $n=2$ is the quaternion group of order $8$.
References
| [a1] | H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1974) ISBN 0-521-20125-X Zbl 0732.51002 |
How to Cite This Entry:
Dicyclic group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dicyclic_group&oldid=51420
Dicyclic group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dicyclic_group&oldid=51420