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- W2885648203 abstract "In this chapter we will describe what is known about the structure of Orth(G) for G a group of small order. Much of this knowledge is the result of computer searches. We will summarize known values and bounds for |Orth(G)| and ω(G) when |G|≤ 23. We will see that order 23 marks a divide. We can find values of |Orth(G)| in the literature for every group of order 23 or less, but we can find no such value for any group of order 24, other than the cyclic group of order 25 and those that have cyclic Sylow 2-subgroups and hence do not admit orthomorphisms. It will be seen that we know ω(G) for all abelian groups G of order 19 or less but can only establish a lower bound for (omega (mathbb {Z}_2times mathbb {Z}_2times mathbb {Z}_5)); and we can only establish lower bounds for ω(G) for nonabelian groups G of order 16. We will also present what is known for groups of order greater than 23. Work on these larger groups has been concentrated on trying to improve lower bounds for ω(G) for groups G that are direct products of elementary abelian groups." @default.
- W2885648203 created "2018-08-22" @default.
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- W2885648203 date "2018-01-01" @default.
- W2885648203 modified "2023-09-27" @default.
- W2885648203 title "Groups of Small Order" @default.
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- W2885648203 doi "https://doi.org/10.1007/978-3-319-94430-2_13" @default.
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