메뉴 건너뛰기




Volumn 200, Issue , 2016, Pages 101-132

Topological groups with many small subgroups

Author keywords

Divisible rank; Divisible weight; Functorial topology; Minimally almost periodic group; Small subgroup generating property; SSGP group; Subgroup interior operator; Subgroup topology; Ulm Kaplanski invariants

Indexed keywords


EID: 84957974930     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2015.12.015     Document Type: Article
Times cited : (10)

References (38)
  • 2
    • 0002524152 scopus 로고
    • Finite Rank Torsion Free Abelian Groups and Rings
    • Springer
    • Arnold D. Finite Rank Torsion Free Abelian Groups and Rings. Lect. Notes Math. 1982, vol. 931. Springer.
    • (1982) Lect. Notes Math. , vol.931
    • Arnold, D.1
  • 4
    • 80053203746 scopus 로고    scopus 로고
    • Interior operators in a category: idempotency and heredity
    • Castellini G. Interior operators in a category: idempotency and heredity. Topol. Appl. 2011, 158:2332-2339.
    • (2011) Topol. Appl. , vol.158 , pp. 2332-2339
    • Castellini, G.1
  • 5
    • 80053185485 scopus 로고
    • Méthodes topologiques en théorie des groupes abéliens
    • Akad. Kiado, Budapest
    • Charles B. Méthodes topologiques en théorie des groupes abéliens. Proceedings of the Colloquium on Abelian Groups 1964, 29-42. Akad. Kiado, Budapest.
    • (1964) Proceedings of the Colloquium on Abelian Groups , pp. 29-42
    • Charles, B.1
  • 6
    • 84943142936 scopus 로고    scopus 로고
    • Some classes of minimally almost periodic topological groups
    • Comfort W.W., Gould F.R. Some classes of minimally almost periodic topological groups. Appl. Gen. Topol. 2015, 16:141-165.
    • (2015) Appl. Gen. Topol. , vol.16 , pp. 141-165
    • Comfort, W.W.1    Gould, F.R.2
  • 11
    • 18444378751 scopus 로고    scopus 로고
    • Forcing hereditarily separable countably compact group topologies on Abelian groups
    • Dikranjan D., Shakhmatov D. Forcing hereditarily separable countably compact group topologies on Abelian groups. Topol. Appl. 2005, 151(1-3):2-54.
    • (2005) Topol. Appl. , vol.151 , Issue.1-3 , pp. 2-54
    • Dikranjan, D.1    Shakhmatov, D.2
  • 12
    • 44349164397 scopus 로고    scopus 로고
    • Reflection principle characterizing groups in which unconditionally closed sets are algebraic
    • Dikranjan D., Shakhmatov D. Reflection principle characterizing groups in which unconditionally closed sets are algebraic. J. Group Theory 2008, 11(3):421-442.
    • (2008) J. Group Theory , vol.11 , Issue.3 , pp. 421-442
    • Dikranjan, D.1    Shakhmatov, D.2
  • 13
    • 77955303877 scopus 로고    scopus 로고
    • The Markov-Zariski topology of an abelian group
    • Dikranjan D., Shakhmatov D. The Markov-Zariski topology of an abelian group. J. Algebra 2010, 324(6):1125-1158.
    • (2010) J. Algebra , vol.324 , Issue.6 , pp. 1125-1158
    • Dikranjan, D.1    Shakhmatov, D.2
  • 14
    • 77952041753 scopus 로고    scopus 로고
    • Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov's potential density
    • Dikranjan D., Shakhmatov D. Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov's potential density. Proc. Am. Math. Soc. 2010, 138:2979-2990.
    • (2010) Proc. Am. Math. Soc. , vol.138 , pp. 2979-2990
    • Dikranjan, D.1    Shakhmatov, D.2
  • 15
    • 79952037927 scopus 로고    scopus 로고
    • A Kronecker-Weyl theorem for subsets of abelian groups
    • Dikranjan D., Shakhmatov D. A Kronecker-Weyl theorem for subsets of abelian groups. Adv. Math. 2011, 226:4776-4795.
    • (2011) Adv. Math. , vol.226 , pp. 4776-4795
    • Dikranjan, D.1    Shakhmatov, D.2
  • 16
    • 84943604754 scopus 로고    scopus 로고
    • A complete solution of Markov's problem on connected group topologies
    • Dikranjan D., Shakhmatov D. A complete solution of Markov's problem on connected group topologies. Adv. Math. 2016, 286:286-307.
    • (2016) Adv. Math. , vol.286 , pp. 286-307
    • Dikranjan, D.1    Shakhmatov, D.2
  • 18
    • 84957997904 scopus 로고    scopus 로고
    • von Neumann kernel, minimal almost periodicity and Zariski topology of the abelian groups
    • work in progress.
    • D. Dikranjan, D. Shakhmatov, von Neumann kernel, minimal almost periodicity and Zariski topology of the abelian groups, work in progress.
    • Dikranjan, D.1    Shakhmatov, D.2
  • 19
    • 0037819490 scopus 로고
    • Categorical Structure of Closure Operators. With Applications to Topology, Algebra and Discrete Mathematics
    • Kluwer, Dordrecht
    • Dikranjan D., Tholen W. Categorical Structure of Closure Operators. With Applications to Topology, Algebra and Discrete Mathematics. Math. Appl. 1995, vol. 346. Kluwer, Dordrecht.
    • (1995) Math. Appl. , vol.346
    • Dikranjan, D.1    Tholen, W.2
  • 20
    • 84936791600 scopus 로고    scopus 로고
    • Closure operators and dual closure operators
    • Dikranjan D., Tholen W. Closure operators and dual closure operators. J. Algebra 2015, 439:373-416.
    • (2015) J. Algebra , vol.439 , pp. 373-416
    • Dikranjan, D.1    Tholen, W.2
  • 21
    • 84957997905 scopus 로고    scopus 로고
    • Closure operators vs interior operators
    • work in progress.
    • D. Dikranjan, W. Tholen, Closure operators vs interior operators, work in progress.
    • Dikranjan, D.1    Tholen, W.2
  • 22
  • 24
    • 84907795720 scopus 로고    scopus 로고
    • Bounded subgroups as a von Neumann radical of an Abelian group
    • Gabriyelyan S. Bounded subgroups as a von Neumann radical of an Abelian group. Topol. Appl. 2014, 178:185-199.
    • (2014) Topol. Appl. , vol.178 , pp. 185-199
    • Gabriyelyan, S.1
  • 25
    • 0001678313 scopus 로고
    • Topological group structures of infinite symmetric groups
    • Gaughan E. Topological group structures of infinite symmetric groups. Proc. Natl. Acad. Sci. USA 1967, 58:907-910.
    • (1967) Proc. Natl. Acad. Sci. USA , vol.58 , pp. 907-910
    • Gaughan, E.1
  • 27
    • 84904804729 scopus 로고    scopus 로고
    • An SSGP topology for Zω
    • Gould F. An SSGP topology for Zω. Topol. Proc. 2014, 44:389-392.
    • (2014) Topol. Proc. , vol.44 , pp. 389-392
    • Gould, F.1
  • 28
    • 0011325578 scopus 로고
    • On the imbedding of topological groups into connected topological groups
    • Hartman S., Mycielski J. On the imbedding of topological groups into connected topological groups. Colloq. Math. 1958, 5:167-169.
    • (1958) Colloq. Math. , vol.5 , pp. 167-169
    • Hartman, S.1    Mycielski, J.2
  • 30
    • 80053203083 scopus 로고    scopus 로고
    • Categorical neighborhood operators
    • Holgate D., Šlapal J. Categorical neighborhood operators. Topol. Appl. 2011, 158:2356-2365.
    • (2011) Topol. Appl. , vol.158 , pp. 2356-2365
    • Holgate, D.1    Šlapal, J.2
  • 31
    • 0002085637 scopus 로고
    • Basic concepts of functorial topologies
    • Springer, Berlin-New York, Abelian Group Theory
    • Mader A. Basic concepts of functorial topologies. Lect. Notes Math. 1981, vol. 874:251-271. Springer, Berlin-New York.
    • (1981) Lect. Notes Math. , vol.874 , pp. 251-271
    • Mader, A.1
  • 32
    • 84968480677 scopus 로고
    • Almost periodic functions in a group I
    • von Neumann J. Almost periodic functions in a group I. Trans. Am. Math. Soc. 1934, 36:445-492.
    • (1934) Trans. Am. Math. Soc. , vol.36 , pp. 445-492
    • von Neumann, J.1
  • 33
    • 0000408579 scopus 로고
    • Minimally almost periodic groups
    • von Neumann J., Wigner E. Minimally almost periodic groups. Ann. Math. (2) 1940, 41:746-750.
    • (1940) Ann. Math. (2) , vol.41 , pp. 746-750
    • von Neumann, J.1    Wigner, E.2
  • 34
    • 33746715495 scopus 로고
    • A solenoidal and monothetic minimally almost periodic group
    • Nienhuys J. A solenoidal and monothetic minimally almost periodic group. Fundam. Math. 1971, 73:167-169.
    • (1971) Fundam. Math. , vol.73 , pp. 167-169
    • Nienhuys, J.1
  • 37
    • 0038785659 scopus 로고
    • On the basic subgroups of abelian p-groups
    • Szele T. On the basic subgroups of abelian p-groups. Acta Math. Acad. Sci. Hung. 1954, 5:129-141.
    • (1954) Acta Math. Acad. Sci. Hung. , vol.5 , pp. 129-141
    • Szele, T.1
  • 38
    • 79955418473 scopus 로고    scopus 로고
    • Interior operators in general categories
    • Vorster S.J.R. Interior operators in general categories. Quaest. Math. 2000, 23:405-416.
    • (2000) Quaest. Math. , vol.23 , pp. 405-416
    • Vorster, S.J.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.