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This question is a generalisation of this one. Let $ G$ be a finite, transitive permutation group. If the point stabiliser $ G_x$ is some faithful permutation representation of a cyclic group $ C_k$ (with possibly more than one orbit), what can $ G_x$ and $ G$ be?Read more

“Let $ G$ be a transitive group of permutations on a given set of letters. Let a new fixed letter be adjoined to every permutation of $ G$ . Then a transitive group $ H$ of permutations on the combined set of letters is called a transitive extension of $ G$ if it contains $Read more

Cyclic cohomology may be defined in several ways: the easiest way to define it is via a subcomplex $ C^*_{\lambda}$ of Hochschild complex consisting from cyclic cochains. There are also other definitions for example using the cyclic bicomplex or $ (b,B)$ (mixed) complex. Relevant definition can be found here. One can define the so calledRead more

Consider $ D_{12}$ the dihedral group of order 12. This is the group of symmetries of the regular hexagon. Label the vertices of the hexagon clockwise as 1, 2, 3, 4, 5, 6. Let σ = (1 2 3 4 5 6) and τ = (2 6)(3 5). Regard $ D_{12}$ as the group $Read more

Let $ G$ be a finite non-Dedekind $ p$ -group with non-cyclic center, where $ p$ is an odd prime. By $ [\langle x\rangle]_G=\{g^{-1}\langle x\rangle g\ |\ g\in G\},$ I mean the conjugacy class of the subgroup $ \langle x\rangle$ of $ G$ and $ U=\{[\langle x\rangle]_G\ |\ \langle x\rangle\ntrianglelefteq G\}$ is the set ofRead more

Hey guys so just yesterday I did a test. But there was something strange about this question. Can you guys tell me the answer because I just put down x, as I had no clue how to do it. Also can you put down the geometric reasons? Also the rectangle is meant to be aRead more