Direct limits and fixed point sets

Journal of Algebra

Volumn 292, Issue 2, 2005, Pages 592-614

  Bergman, George M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Action of a group or monoid on a set; Commutativity of limits with direct limits (filtered colimits); Partially ordered set; Set valued functor on a category

Indexed keywords

EID: 25144497438     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2005.08.002     Document Type: Article

References (20)

1. G.M. Bergman An Invitation to General Algebra and Universal Constructions 1998 pub. Henry Helson Berkeley, CA Readable online at http://math.berkeley.edu/~gbergman/245 MR 99h:18001
2. G.M. Bergman Generating infinite symmetric groups J. London Math. Soc., in press. Preprint version, 9 pp. http://math.berkeley.edu/~gbergman/ papers/Sym_OmegM:1. {tex,dvi,ps} arXiv: math.GR/0401304
3. S. Bigelow Supplements of bounded permutation groups J. Symbolic Logic 63 1998 89-102 MR 99b:20007.
4. A.H. Clifford G.B. Preston The Algebraic Theory of Semigroups, vol. II Math. Surveys vol. 7 1967 Amer. Math. Soc. xv+350 pp. MR 36#1158
5. M. Droste R. Göbel Uncountable cofinalities of permutation groups J. London Math. Soc. (2) 71 2005 335-344 MR 2122432.
6. M. Droste W.C. Holland Generating automorphism groups of chains Forum Math. 17 2005 699-710
7. P. Dubreil Contribution à la théorie des demi-groupes Mém. Acad. Sci. Inst. France (2) 63 1941 52 pp. MR 8,15a
8. R. El Bashir T. Kepka P. Němec Modules commuting (via Hom) with some colimits Czechoslovak Math. J. 53 128 2003 891-905 MR 2004i:16002.
9. A. Grothendieck Sur quelques points d'algèbre homologique Tôhoku Math. J. 9 1957 119-221 MR 21#1328
10. R. Hartshorne Algebraic Geometry Grad. Texts in Math. vol. 52 1977 Springer MR 57#3116
11. E. Hotzel On semigroups with maximal conditions Semigroup Forum 11 1975/ 76 337-362 MR 52#10921
12. G.M. Kelly Basic Concepts of Enriched Category Theory London Math. Soc. Lecture Note Ser. vol. 64 1982 MR 84e:18001. Readable at http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html
13. S. Koppelberg J. Tits Une propriété des produits directs infinis de groupes finis isomorphes C. R. Acad. Sci. Paris Sér. A 279 1974 583-585 MR 51#13058
14. I.B. Kozhukhov Semigroups with certain conditions on congruences J. Math. Sci. (New York) 114 2003 1119-1126 MR 2004b:20087
15. S. Mac Lane Categories for the Working Mathematician Grad. Texts in Math. vol. 5 1971 Springer MR 50#7275
16. H.D. Macpherson P.M. Neumann Subgroups of infinite symmetric groups J. London Math. Soc. (2) 42 1990 64-84 MR 92d:20006 (Note: As pointed out in [3], Theorem 1.2 of this paper requires additional set-theoretic hypotheses for some K.).
17. Open problems discussed at a conference in honor of Walter Taylor at the University of Colorado, 15-18 August, 2004, 7 pp. http://math.berkeley.edu/~gbergman/papers/WTq. {tex,dvi,ps,pdf}
18. B.M. Schein Stationary subsets, stabilizers and transitive representations of semigroups Dissertationes Math. (Rozprawy Mat.) 77 1970 38 MR 44#4129
19. S. Shelah On a problem of Kurosh, Jónsson groups, and applications, in: Word Problems II Conf. on Decision Problems in Algebra, Oxford, 1976 in: Stud. Logic Found. Math. vol. 95 1980 North-Holland pp. 373-394 MR 81j:20047.
20. S. Thomas The cofinalities of the infinite-dimensional classical groups J. Algebra 179 1996 704-719 MR 96k:20005.