I am reading this paper where the object $C_4\times C_2 : C_2$ is used as a group structure. I know that $C_n$ is a cyclic group but don't know what kind of operation between groups is identified by the symbol "$:$". Does anyone know about that? Thanks to everyone for the help.
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$\begingroup$ This paper : worldscientific.com/doi/abs/10.1142/S0219498816501759 $\endgroup$– N mathCommented Feb 23, 2020 at 11:47
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2$\begingroup$ As noted in the answer below, it's semidirect product, but does not specify which one. This list of groups of order 16 might be helpful: people.maths.bris.ac.uk/~matyd/GroupNames/index.html#order16 The "aliases" feature is particularly useful. $\endgroup$– Henri JohnstonCommented Feb 23, 2020 at 18:48
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$\begingroup$ @Henri Johnston Thanks for the link. $\endgroup$– N mathCommented Feb 25, 2020 at 9:05
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1 Answer
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The colon means "semidirect product", but it does not specify which semidirect product. This notation is a concise shorthand that gives important structural information without necessarily uniquely specifying the group. You can read more about similar notation conventions in the introduction to the ATLAS of finite groups.
answered Feb 23, 2020 at 12:21