Automorphisms of metacyclic groups
Haimiao Chen; Yueshan Xiong; Zhongjian Zhu
Czechoslovak Mathematical Journal (2018)
- Volume: 68, Issue: 3, page 803-815
- ISSN: 0011-4642
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topChen, Haimiao, Xiong, Yueshan, and Zhu, Zhongjian. "Automorphisms of metacyclic groups." Czechoslovak Mathematical Journal 68.3 (2018): 803-815. <http://eudml.org/doc/294178>.
@article{Chen2018,
abstract = {A metacyclic group $H$ can be presented as $\langle \alpha ,\beta \colon \alpha ^\{n\}=1$, $ \beta ^\{m\}=\alpha ^\{t\}$, $\beta \alpha \beta ^\{-1\}=\alpha ^\{r\}\rangle $ for some $n$, $m$, $t$, $r$. Each endomorphism $\sigma $ of $H$ is determined by $\sigma (\alpha )=\alpha ^\{x_\{1\}\}\beta ^\{y_\{1\}\}$, $ \sigma (\beta )=\alpha ^\{x_\{2\}\}\beta ^\{y_\{2\}\}$ for some integers $x_\{1\}$, $x_\{2\}$, $y_\{1\}$, $y_\{2\}$. We give sufficient and necessary conditions on $x_\{1\}$, $x_\{2\}$, $y_\{1\}$, $y_\{2\}$ for $\sigma $ to be an automorphism.},
author = {Chen, Haimiao, Xiong, Yueshan, Zhu, Zhongjian},
journal = {Czechoslovak Mathematical Journal},
keywords = {automorphism; metacyclic group; linear congruence equation},
language = {eng},
number = {3},
pages = {803-815},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Automorphisms of metacyclic groups},
url = {http://eudml.org/doc/294178},
volume = {68},
year = {2018},
}
TY - JOUR
AU - Chen, Haimiao
AU - Xiong, Yueshan
AU - Zhu, Zhongjian
TI - Automorphisms of metacyclic groups
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 803
EP - 815
AB - A metacyclic group $H$ can be presented as $\langle \alpha ,\beta \colon \alpha ^{n}=1$, $ \beta ^{m}=\alpha ^{t}$, $\beta \alpha \beta ^{-1}=\alpha ^{r}\rangle $ for some $n$, $m$, $t$, $r$. Each endomorphism $\sigma $ of $H$ is determined by $\sigma (\alpha )=\alpha ^{x_{1}}\beta ^{y_{1}}$, $ \sigma (\beta )=\alpha ^{x_{2}}\beta ^{y_{2}}$ for some integers $x_{1}$, $x_{2}$, $y_{1}$, $y_{2}$. We give sufficient and necessary conditions on $x_{1}$, $x_{2}$, $y_{1}$, $y_{2}$ for $\sigma $ to be an automorphism.
LA - eng
KW - automorphism; metacyclic group; linear congruence equation
UR - http://eudml.org/doc/294178
ER -
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