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A result about cosets

John C. Lennox, James Wiegold (1995)

Rendiconti del Seminario Matematico della Università di Padova

Central sequences in the factor associated with Thompson’s group F

Paul Jolissaint (1998)

Annales de l'institut Fourier

We prove that the type II 1 factor L ( F ) generated by the regular representation of F is isomorphic to its tensor product with the hyperfinite type II 1 factor. This implies that the unitary group of L ( F ) is contractible with respect to the topology defined by the natural Hilbertian norm.

Characterizing finite groups whose enhanced power graphs have universal vertices

David G. Costanzo, Mark L. Lewis, Stefano Schmidt, Eyob Tsegaye, Gabe Udell (2024)

Czechoslovak Mathematical Journal

Let G be a finite group and construct a graph Δ ( G ) by taking G { 1 } as the vertex set of Δ ( G ) and by drawing an edge between two vertices x and y if x , y is cyclic. Let K ( G ) be the set consisting of the universal vertices of Δ ( G ) along the identity element. For a solvable group G , we present a necessary and sufficient condition for K ( G ) to be nontrivial. We also develop a connection between Δ ( G ) and K ( G ) when | G | is divisible by two distinct primes and the diameter of Δ ( G ) is 2.

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