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Showing 1 to 4 of 4 for “"Profinite groups"”.
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A Classifying Family of Spaces for the Cohomology of Profinite Groups
… a classifying space also apply to topological groups, the relationship of the resulting space to the group's cohomology is unclear. Profinite groups are a special case of topological groups, determined entirely as the limits of inverse systems of finite, discrete groups. The goal of this work …
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On an analogue to the Grushko-Neumann theorem involving finite groups
Let C be a class of finite groups closed under the operations of taking subgroups, quotients, and extensions. Let H and K be pro-C-groups and let $G=H*K$ be their free pro-C-product. An open question in the theory of profinite groups is whether or not $d(G)=d(H)+d(K),$ which is an analogue to the …
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Representations of Fundamental Groups of Abelian Varieties in Characteristic P
… from certain semidirect products of profinite groups into finite groups. As a corollary, we deduce that when $\lambda=0$, \[\frac{\#\Hom(\pi_1^{\text{\'et}}(A_g),GL_n(\mathbb F_q))}{\#GL_n(\mathbb F_q)}\] is a Laurent polynomial in $q$.
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A measure for the number of commuting subgroups in compact groups
… which counts the pairs of closed commuting subgroups in infinite groups. This measure turns out to be an extension of what was known in the finite case as subgroup commutativity degree and opens a new approach of study for the class of near abelian groups, recently introduced in [24, 27]. The …