Groups all proper quotient groups of which possess layer-Chernikov properties

N. V. Kalashnikova

doi:10.1007/bf02524477

Groups all proper quotient groups of which possess layer-Chernikov properties

Ukrainian Mathematical Journal ◽

10.1007/bf02524477 ◽

1998 ◽

Vol 50 (11) ◽

pp. 1710-1718

Author(s):

N. V. Kalashnikova

Keyword(s):

Quotient Groups ◽

Proper Quotient

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Groups with Hypercyclic Proper Quotient Groups

Ukrainian Mathematical Journal ◽

10.1023/b:ukma.0000010157.64107.1d ◽

2003 ◽

Vol 55 (4) ◽

pp. 566-575

Author(s):

L. A. Kurdachenko ◽

P. Soules

Keyword(s):

Quotient Groups ◽

Proper Quotient

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Finitep-Groups All of Whose Proper Quotient Groups are Abelian or Inner-Abelian

Communications in Algebra ◽

10.1080/00927870903074066 ◽

2010 ◽

Vol 38 (8) ◽

pp. 2797-2807 ◽

Cited By ~ 1

Author(s):

Qinhai Zhang ◽

Lili Li ◽

Mingyao Xu

Keyword(s):

Quotient Groups ◽

Proper Quotient

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A Survey on Just-Non-𝔛Groups

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2010/190830 ◽

2010 ◽

Vol 2010 ◽

pp. 1-8

Author(s):

Daniele Ettore Otera ◽

Francesco G. Russo

Keyword(s):

Present Note ◽

Topological Groups ◽

Quotient Groups ◽

Proper Quotient

Let𝔛be a class of groups. A group which does not belong to𝔛but all of whose proper quotient groups belong to𝔛is called just-non-𝔛group. The present note is a survey of recent results on the topic with a special attention to topological groups.

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On varieties of metabelian p-groups, and their laws

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700005103 ◽

1967 ◽

Vol 7 (1) ◽

pp. 64-80 ◽

Cited By ~ 16

Author(s):

Warren Brisley

Keyword(s):

Critical Group ◽

Proper Factor ◽

Simple Basis ◽

Quotient Groups ◽

Proper Quotient

The purpose of this article is to present some results on varieties of metabelian p-groups, nilpotent of class c, with the prime p greater than c. After some preliminary lemmas in § 3, it is established in § 4, Theorem 3, that there is a simple basis for the laws of such a variety, and this basis is explicitly stated. This allows the description of the lattice of such varieties, and in § 5, Theorem 4, it is shown that each such variety has a two-generator member which generates it; this is established by the help of Theorem 5, which states that each critical group is a two-generator group, and Theorem 6, which gives explicitly the varieties generated by the proper subgroups, by the proper quotient groups, and by the proper factor groups of such a critical group.

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