Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups

Fausto De Mari

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 853-866
  • ISSN: 0392-4041

Abstract

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In this paper, (generalized) soluble groups for which the set of all subgroups having infinite index in their normal closure satisfies some weak chain condition are described.

How to cite

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De Mari, Fausto. "Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 853-866. <http://eudml.org/doc/290412>.

@article{DeMari2007,
abstract = {In this paper, (generalized) soluble groups for which the set of all subgroups having infinite index in their normal closure satisfies some weak chain condition are described.},
author = {De Mari, Fausto},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {853-866},
publisher = {Unione Matematica Italiana},
title = {Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups},
url = {http://eudml.org/doc/290412},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - De Mari, Fausto
TI - Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 853
EP - 866
AB - In this paper, (generalized) soluble groups for which the set of all subgroups having infinite index in their normal closure satisfies some weak chain condition are described.
LA - eng
UR - http://eudml.org/doc/290412
ER -

References

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  1. AMBERG, B., Fast-Polyminimaxgruppen, Math. Ann., 175 (1968), 44-49. MR223454DOI10.1007/BF01350808
  2. BAER, R., Polyminimaxgruppen, Math. Ann., 175 (1968), 1-43. MR223453DOI10.1007/BF01350807
  3. CARIN, V. S., On soluble groups of type A 3 , Mat. Sb., 54 (1961), 489-499. MR138685
  4. CUTOLO, G. - KURDACHENKO, L. A., Weak chain conditions for non-almost normal subgroups, Proceedings of Groups St. Andrews in Galway, Cambridge University Press (1993), 120-130. Zbl0843.20020MR1342785DOI10.1017/CBO9780511629280.012
  5. DE MARI, F. - DE GIOVANNI, F., Double chain conditions for infinite groups, Ricerche Mat., 54 (2005), 59-70. Zbl1142.20010MR2290204
  6. FRANCIOSI, S. - DE GIOVANNI, F., Groups satisfying the minimal condition on certain non-normal subgroups, Proceedings of Groups Korea 1994, de Gruyter (1995), 107-118. Zbl0868.20031MR1476951
  7. GALOPPO, A., Groups satisfying the maximal condition on non-nearly normal subgroups, Ricerche Mat., 49 (2000), 213-220. Zbl1163.20308MR1848347
  8. NEUMANN, B. H., Groups with finite classes of conjugate subgroups, Math Z., 63 (1955), 76-96. Zbl0064.25201MR72137DOI10.1007/BF01187925
  9. ROBINSON, D. J. S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972). Zbl0243.20032MR332990
  10. SHORES, T. S., A chain condition for groups, Rocky Mountain J. Math., 3 (1973), 83-89. Zbl0256.20034MR347984DOI10.1216/RMJ-1973-3-1-83
  11. ŠUNKOV, V. P., Locally finite groups with a minimality condition for abelian subgroups, Algebra and Logic, 9 (1970), 350-370. MR283063
  12. ZAIČEV, D. I., Groups satisfying a weak minimum condition, Soviet Math. Dokl., 9 (1968), 194-197. 
  13. ZAIČEV, D. I., On groups which satisfy a weak minimality condition, Math. USSR Sb., 7 (1969), 315-322. 
  14. ZAIČEV, D. I., Theory of minimax groups, Ukrainian Math. J., 23 (1971), 536-542. 

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