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Mathematics LibreTexts

10: Normal Subgroups and Factor Groups

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If H is a subgroup of a group G, then right cosets are not always the same as left cosets; that is, it is not always the case that gH=Hg for all gG. The subgroups for which this property holds play a critical role in group theory—they allow for the construction of a new class of groups, called factor or quotient groups. Factor groups may be studied directly or by using homomorphisms, a generalization of isomorphisms. We will study homomorphisms in Chapter 11.


This page titled 10: Normal Subgroups and Factor Groups is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Thomas W. Judson (Abstract Algebra: Theory and Applications) via source content that was edited to the style and standards of the LibreTexts platform.

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