# Nilpotent inverse semigroups with central idempotents

@article{Kowol1982NilpotentIS, title={Nilpotent inverse semigroups with central idempotents}, author={Gerhard Kowol and Heinz Mitsch}, journal={Transactions of the American Mathematical Society}, year={1982}, volume={271}, pages={437-449} }

An inverse semigroup S with central idempotents, i.e. a strong semilattice of groups, will be called nilpotent, if it is finite and if for each prime divisor p¡ of the orders of the structure groups of S the sets P¡ = {s G S\ o(s) = pf", ks > 0} are subsemigroups of S. If 5 is a group, then P¡ are exactly the Sylow />,-subgroups of the group. A theory similar to that given by W. Burnside for finite nilpotcnt groups is developed introducing the concepts of ascending resp. descending central…

## 5 Citations

### Inverse semigroups with idempotent-fixing automorphisms

- Mathematics
- 2013

A celebrated result of J. Thompson says that if a finite group $$G$$G has a fixed-point-free automorphism of prime order, then $$G$$G is nilpotent. The main purpose of this note is to extend this…

### Inverse Semigroups with Idempotent-Fixing

- Mathematics
- 2015

A celebrated result of J. Thompson says that if a finite group G has a fixed-point-free automorphism of prime order, then G is nilpotent. The main purpose of this note is to extend this result to…

### Inverse semigroups all of whose proper homomorphic images are groups

- MathematicsBulletin of the Australian Mathematical Society
- 2004

We characterise those inverse semigroups whose proper(non-isomorphic) homomorphic images are all groups. We also show that the bicyclic semigroup is the only such semigroup in certain cases.

### Abelianness and centrality in inverse semigroups

- Mathematics
- 2022

. We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding…

### Inverse semigroups with idempotent-fixing automorphisms

- Mathematics, Materials ScienceSemigroup Forum
- 2014

A celebrated result of J. Thompson says that if a finite group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

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A congruence ρ on a semigroup will be called idempotent-separating if each ρ-class contains at most one idempotent. It is shown below that there exists a maximum such congruence µ on every inverse…

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It is seen almost immediately (Theorem 1) that S admits relative inverses if and only if it is the class sum of mutually disjoint groups S., one to each idempotent element e of S. This fact tells us…

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