Local Sylow theory of totally disconnected, locally compact groups

Reid, Colin
(2013) Journal of Group Theory — Vol. 16, n° 4, p. 535-555 (2013)

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  • Reid, ColinUCLouvain
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Abstract
We define a local Sylow subgroup of a totally disconnected, locally compact (t.d.l.c.) group G to be a maximal pro-p subgroup of an open compact subgroup of G. We use these subgroups to define the p-localization of G, a locally virtually pro-p group which maps continuously and injectively to G with dense image, and describe the relationship between the scale and modular functions of G and those of its p-localization. In the case of locally virtually prosoluble groups, we consider all primes simultaneously using local Sylow bases. © de Gruyter 2013.
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Reid, C. (2013). Local Sylow theory of totally disconnected, locally compact groups. Journal of Group Theory, 16(4), 535-555. https://doi.org/10.1515/jgt-2013-0005 (Original work published 2013)