Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You and Your Team.

Learn More →

The homomorphic images of infinite symmetric groups

The homomorphic images of infinite symmetric groups Abstract. We give a solution of De Bruijn's problem s to which homomorphic images of an infinite Symmetrie group S () are embeddable into S (). We prove (in ZF -f V = L) that $()/$() can be embedded into S () if and only if < cf (). We also discuss F.Clare's problem whether S(K)/SK () is a universal group. We prove that it is consistent with ZFC that 8()/8() is not universal. However S(K)/SK(K) is almost universal, since the group SK+ (+) of all bounded permutations of + embeds into it when is regul r. 1991 Mathematics Subject Classification: 20B30; 20A15, 03E05. 1. Introduction In its long history of more than 150 years the theory of finite permutation groups has reached a high level of perfection. During this rather long period only few authors also studied infinite permutation groups. A reason for this apparent disproportion may be that the rieh machinery of finite combinatorics and number theory was at band to all mathematicians while the powerful methods of infinite combinatorics (set theory) remained unknown to most of them. Without exaggeration one might say that the use of set theory consisted in the use of the bracked http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

The homomorphic images of infinite symmetric groups

Forum Mathematicum , Volume 5 (5) – Jan 1, 1993

Loading next page...
 
/lp/de-gruyter/the-homomorphic-images-of-infinite-symmetric-groups-AS26eTcVJV
Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1993.5.505
Publisher site
See Article on Publisher Site

Abstract

Abstract. We give a solution of De Bruijn's problem s to which homomorphic images of an infinite Symmetrie group S () are embeddable into S (). We prove (in ZF -f V = L) that $()/$() can be embedded into S () if and only if < cf (). We also discuss F.Clare's problem whether S(K)/SK () is a universal group. We prove that it is consistent with ZFC that 8()/8() is not universal. However S(K)/SK(K) is almost universal, since the group SK+ (+) of all bounded permutations of + embeds into it when is regul r. 1991 Mathematics Subject Classification: 20B30; 20A15, 03E05. 1. Introduction In its long history of more than 150 years the theory of finite permutation groups has reached a high level of perfection. During this rather long period only few authors also studied infinite permutation groups. A reason for this apparent disproportion may be that the rieh machinery of finite combinatorics and number theory was at band to all mathematicians while the powerful methods of infinite combinatorics (set theory) remained unknown to most of them. Without exaggeration one might say that the use of set theory consisted in the use of the bracked

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1993

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$499/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month