Introduction:
In this response, we will analyze the given reactions and identify the one that does not produce a ketone as a significant organic product. We will explain why the other reactions do produce a ketone and provide a detailed explanation for each.

Reactions:
1. Oxidation of secondary alcohol: Secondary alcohols can be oxidized to ketones using oxidizing agents such as chromic acid (CrO3) or potassium permanganate (KMnO4). This reaction involves the loss of two hydrogen atoms from the alcohol, resulting in the formation of a ketone. Therefore, this reaction does produce a ketone as a significant organic product.

2. Oxidation of primary alcohol: Primary alcohols can be oxidized to aldehydes using oxidizing agents such as pyridinium chlorochromate (PCC) or Jones reagent (CrO3/H2SO4). Aldehydes can further be oxidized to carboxylic acids, but in this case, we are interested in the formation of ketones. Therefore, this reaction does not produce a ketone as a significant organic product, as the primary alcohol is converted to an aldehyde.

3. Friedel-Crafts acylation: In the Friedel-Crafts acylation reaction, an acyl group (RCO-) is introduced into an aromatic ring using a Lewis acid catalyst such as aluminum chloride (AlCl3). This reaction results in the formation of an aromatic ketone. Therefore, this reaction does produce a ketone as a significant organic product.

4. Wittig reaction: The Wittig reaction involves the conversion of an aldehyde or ketone into an alkene using a phosphonium ylide. This reaction does not produce a ketone as a significant organic product, as the aldehyde or ketone is converted into an alkene.

Conclusion:
Among the given reactions, the oxidation of a primary alcohol is the only reaction that does not produce a ketone as a significant organic product. This reaction results in the formation of an aldehyde rather than a ketone. The other reactions, such as the oxidation of a secondary alcohol, Friedel-Crafts acylation, and Wittig reaction, all produce ketones as significant organic products.