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Abstract If G is permutation group acting on a finite set $$\Omega $$ , then this action induces a natural action of G on the power set $$\mathscr{P}(\Omega )$$ . The number $s(G)$ of orbits in this action is an important parameter that has been used in bounding numbers of conjugacy classes in finite groups. In this context, $$\inf ({\log _2 s(G)}/{\log _2 |G|})$$ plays a role, but the precise value of this constant was unknown. We determine it where G runs over all permutation groups not containing any $${{\textrm {A}}}_l, l> 4$$ , as a composition factor.
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Lifting N∞ operads from conjugacydata
We isolate a class of groups — called lossless groups — for which homotopy classes of G-N∞ operads are in bijection with certain restricted transfer systems on the poset of conjugacy classes Sub(G)/G.
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- Award ID(s):
- 2204365
- PAR ID:
- 10536038
- Publisher / Repository:
- Mathematical Sciences Publishers
- Date Published:
- Journal Name:
- Tunisian Journal of Mathematics
- Volume:
- 5
- Issue:
- 3
- ISSN:
- 2576-7658
- Page Range / eLocation ID:
- 479 to 504
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.2140/tunis.2023.5.479
