Generating "large" subgroups and subsemigroups

Group theory;Semigroups

Jonušas, Julius ; Mitchell, James David ; Mitchell, James David

University:University of St Andrews

Department:Mathematics & Statistics (School of)

关键词: Group theory;    Semigroups;   

Others  :  https://research-repository.st-andrews.ac.uk/bitstream/handle/10023/9913/JuliusJonusasPhDThesis.pdf?sequence=2&isAllowed=y

来源: DR-NTU

【 摘 要 】

In this thesis we will be exclusively considering uncountable groups and semigroups.Roughly speaking the underlying problem is to find “large” subgroups(or subsemigroups) of the object in question, where we consider three differentnotions of “largeness”: (i) We classify all the subsemigroups of the set of all mapping from a countableset back to itself which contains a specific uncountable subsemigroup; (ii) We investigate topological “largeness”, in particular subgroups which arefinitely generated and dense; (iii) We investigate if it is possible to find an integer r such that any countablecollection of elements belongs to some r-generated subsemigroup, and moreprecisely can these elements be obtained by multiplying the generators in aprescribed fashion.