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On relative ranks of full transformation semigroups

 

作者: John M. Howie,   N. Ruškuc,   P.M. Higgins,  

 

期刊: Communications in Algebra  （Taylor Available online 1998）
卷期: Volume 26, issue 3  

页码: 733-748

 

ISSN:0092-7872

 

年代: 1998

 

DOI:10.1080/00927879808826160

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: semigroup;mapping;rank;bijection;idempotent;cardinal number;20M20;04A05

 

数据来源: Taylor

 

摘要:

For a semigroupSand a setthe relative rank ofSmoduloAis the minimal cardinality of a setBsuch thatgeneratesS. We show that the relative rank of an infinite full transformation semigroup modulo the symmetric group, and also modulo the set of all idempotent mappings, is equal to 2. We also characterise all pairs of mappings which, together with the symmetric group or the set of all idempotents, generate the full transformation semigroup.

 

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