The seriality problem for Sylow-permutable subgroups in locally finite groups

Derek J. S. Robinson (University of Illinois at Urbana-Champaign)

05-Nov-2020, 16:00-17:00 (3 years ago)

Abstract: A subgroup $H$ of a group $G$ is said to be weakly Sylow permutable in $G$ if $HP=PH$ for all Sylow subgroups $P$ of $G$ and all primes $p$ dividing orders of elements of $H$. Otto Kegel proved that if $G$ is finite, then $H$ is subnormal in $G$. This does not hold for infinite groups. The Seriality Problem is whether Kegel’s theorem can be extended to locally finite groups if "subnormal” is replaced by “serial”. I will discuss the background to the problem and recent progress towards its solution.

group theory

Audience: researchers in the topic


GOThIC - Ischia Online Group Theory Conference

Series comments: Please send a message to andrea.caranti@unitn.it to receive a link to the Zoom room where the conference (a series of talks, actually) takes place.

Organizer: Andrea Caranti*
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