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The Classification Problem for Groups

In: Fundamentals of Group Theory

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  • Steven Roman

Abstract

One of the most important outstanding problems of group theory is the problem of classifying all groups up to isomorphism. This is the classification problem for groups. More precisely, isomorphism of groups is an equivalence relation. Therefore, a set of canonical forms or a complete invariant constitutes a theoretical solution to the classification problem for groups. Of course, it may not be a practical solution unless some form of “algorithm” is available for determining the canonical form or invariant of any group.

Suggested Citation

  • Steven Roman, 2012. "The Classification Problem for Groups," Springer Books, in: Fundamentals of Group Theory, edition 1, chapter 0, pages 263-271, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8301-6_9
    DOI: 10.1007/978-0-8176-8301-6_9
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