Complete universal locally finite groups

Author:
Ken Hickin

Journal:
Trans. Amer. Math. Soc. **239** (1978), 213-227

MSC:
Primary 20E25; Secondary 20F50

DOI:
https://doi.org/10.1090/S0002-9947-1978-0480750-4

MathSciNet review:
0480750

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper will partly strengthen a recent application of model theory to the construction of sets of pairwise nonembeddable universal locally finite groups [8]. Our result is

Theorem. *There is a set* *of* *universal locally finite groups of order* *with the following properties*:

0.1. *If* *and A and B are uncountable sugroups of U and V, then A and B are not isomorphic. Let A be an uncountable subgroup of* .

0.2. *A does not belong to any proper variety of groups, and*

0.3. *A is not isomorphic to any of its proper subgroups*.

0.4. *Every* *is a complete group* (*every automorphism of U is inner*).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0480750-4

Keywords:
Locally finite groups,
universal homogeneous groups,
complete groups,
subgroup-incomparability,
regular representation,
group amalgams

Article copyright:
© Copyright 1978
American Mathematical Society