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The subnormal coalescence of some classes of groups of finite rank

  • Mark Drukker (a1), Derek J. S. Robinson (a1) and Ian Stewart (a2)
Abstract

A class of groups forms a (subnormal) coalition class, or is (subnormally) coalescent, if whenever H and K are subnormal -subgroups of a group G then their join <H, K> is also a subnormal -subgroup of G. Among the known coalition classes are those of finite groups and polycylic groups (Wielandt [15]); groups with maximal condition for subgroups (Baer [1]); finitely generated nilpotent groups (Baer [2]); groups with maximal or minimal condition on subnormal subgroups (Robinson [8], Roseblade [11, 12]); minimax groups (Roseblade, unpublished); and any subjunctive class of finitely generated groups (Roseblade and Stonehewer [13]).

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] R. Baer , ‘Lokal Noethersche Gruppen’, Math. Z. 66 (1957), 341363.

[2] R. Baer , ‘Nil-Gruppen’, Math. Z. 62 (1955), 402437.

[3] R. Baer , ‘Polyminimaxgruppen’, Math. Ann. 175 (1968), 143.

[4] K. A. Hirsch , ‘Über lokal-nilpotente Gruppen’, Math. Z. 63 (1955), 290294.

[8] D. J. S. Robinson , ‘On the theory of subnormal subgroups’, Math, Z. 89 (1965), 3051.

[12] J. E. Roseblade , ‘A note on subnormal coalition classes’, Math. Z. 90 (1965), 373375.

[13] J. E. Roseblade and S. E. Stonehewer , ‘Subjunctive and locally coalescent classes’, J. Algebra 8 (1968), 423435.

[14] S. E. Stonehewer , ‘The join of finitely many subnormal subgroups’, Bull. London. Math. Soc. 2 (1970), 7782.

[15] H. Wielandt , ‘Eine Verallgemeinerung der invarianten Untergruppen’, Math. Z. 45 (1939), 209244.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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