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Some generalizations of normal series in infinite groups

Published online by Cambridge University Press:  09 April 2009

Richard E. Phillips
Richard E. Phillips
Affiliation:
Department of MathematicsMichigan State University, U.S.A.
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In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G, where for all α < λ, either Gα ⊲ Gα+1 or [Gα+1: Gα] < ∞. If such a series has finite length, A is called F-subnormal in G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 496 - 502
Copyright
Copyright © Australian Mathematical Society 1972

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