Let G be a group, N a normal subgroup of G (for example, N ◁ G) and H a subgroup of G. The following statements are equivalent:
G = NH and N ∩ H =
Although the Unicode description of the rtimes symbol says "right normal factor", a number of authors use it with a left normal factor. Therefore the usual caution for mathematical notation applies: When reading, be careful to notice the conventions adopted by the author, and when writing, explain notation choices for the reader. The choice of symbol may vary, but putting the normal factor on the left seems fairly consistent.
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