An automatic group admits an automatic structure for a group: a regular language of representatives and synchronous group multiplier automata recognizing right multiplication by each generator and equality of representatives. Representatives need not be unique. This finite-state description yields effective algorithms for the word problem for a group.
An "automatic group" can refer to different concepts depending on the context in which it is used. Here are a few possibilities: 1. **Sociology/Psychology**: In social contexts, an automatic group might refer to a category of individuals who are grouped together based on certain inherent characteristics, such as demographic factors (age, gender, etc.). This grouping occurs without intentional or conscious effort on the part of the individuals.
New to topics? Read the docs here!