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sbagley.bsky.social
•
9 days ago
Can't figure out how to use the hypothesis that p is the smallest divisor. 🤔🤔🤔
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profkinyon.bsky.social
•
9 days ago
Consider the action of G on H by conjugation. The size of any orbit is no larger than p and divides |G|. So the hypothesis implies that any nontrivial orbit must have size precisely p. Does that help?
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sbagley.bsky.social
•
9 days ago
Ah, I haven't started thinking about group actions yet this semester, lol.
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profkinyon.bsky.social
•
9 days ago
Oh, well, you can avoid the action jargon:
(1) the size of any conjugacy class divides |G|,
(2) H is a union of conjugacy classes
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(1) the size of any conjugacy class divides |G|,
(2) H is a union of conjugacy classes