Lesson plan
Semipermutable subgroup
In mathematics, in algebra, in the realm of group theory, a subgroup H of a finite group G is said to be semipermutable if H commutes with every subgroup K whose order is relatively prime to that of H . Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.
Article summary
In mathematics, in algebra, in the realm of group theory, a subgroup H of a finite group G is said to be semipermutable if H commutes with every subgroup K whose order is relatively prime to that of H . Clearly, every permutable subgroup of a finite group is semipermutable. The converse, however, is not necessarily true.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.