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In the book "Horizons_ exploring the universe-Cengage learning (2018)", p200, it states that:

Helium fusion produces carbon, and some of the carbon nuclei absorb helium nuclei to form oxygen. A few of the oxygen nuclei can absorb helium nuclei and form neon and then magnesium.

But when I check Wikipedia for Oxygen-burning process, there doesn't seem to have any steps that will produce Neon, but when I check for Carbon-burning process, two carbon-12 nuclei can fuse to a neon and helium nuclei, so is there an error in the book? Or there are other steps of oxygen burning that will produce neon?

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The pages you’re looking at describe fusion of two similar nuclei with each other (e.g. oxygen with oxygen). But fusion doesn’t have to involve identical nuclei, and reactions involving more abundant nuclei will in general occur at a higher rate (though this can vary based on other factors, too).

Long before oxygen-oxygen or neon-neon reactions become important, reactions involving helium nuclei (also called “alpha particles”) take place. That is what the text in your book is referring to: C + He gives O, and O + He gives Ne. See the list in this Wikipedia article on the alpha process.

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