Methanogens do not produce oxygen.

Explanation

**Step-by-Step Solution:**

1. **Understanding Methanogens**: Methanogens are a specific group of microorganisms that belong to the domain Archaea. They are known for their ability to produce methane as a metabolic byproduct.

2. **Anaerobic Nature**: Methanogens are classified as anaerobic bacteria, which means they thrive in environments devoid of oxygen. They do not require oxygen for their survival or metabolic processes.

3. **Metabolic Processes**: The primary metabolic process of methanogens involves the conversion of organic matter into methane. During this process, they may also produce other gases such as hydrogen and hydrogen sulfide.

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