Select the most appropriate one-word substitution for the given group of words. 

To walk aimlessly 

Amble

The most appropriate one-word substitution for the given group of words "To walk aimlessly" is "Wanderer."

Here are the explanations of the four options:

1. Wanderer: A "wanderer" is a person who travels or walks around without a specific destination or purpose. They may explore different places, meander through streets or landscapes, or simply wander without a set direction.

2. Amble: "Amble" refers to a leisurely or relaxed walk, usually without hurrying or a specific purpose. While it implies a slower pace, it does not necessarily convey the notion of walking aimlessly.

3. Trolling: "Trolling" typically refers to the act of intentionally provoking or inciting others online through disruptive or inflammatory comments. It does not relate to walking aimlessly.

4. Jogging: "Jogging" refers to running at a gentle or moderate pace for fitness or exercise purposes. It involves a rhythmic and purposeful stride, which is different from the concept of walking aimlessly.