Basic p-groups: higher commutator structure
نویسندگان
چکیده
منابع مشابه
The Higher Commutator Subgroups of a Group
It is not the object of this address to introduce you to new theories or to tell of great discoveries. Quite on the contrary; I intend to speak of unsolved problems and of conjectures. In order to describe these, certain concepts will have to be discussed ; and for obtaining a proper perspective it will be necessary to mention a number of theorems, some of them new. The proofs of the latter wil...
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a result of dixon, evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $g$ itself has this property, i.e. the commutator subgroup of $g$ has finite rank. it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup, then also the commutator s...
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The study of associativity of the commutator operation in groups goes back to the work of F. W. Levi in 1942. In the 1960’s Richard J. Thompson created a group F whose elements are representatives of the generalized associative law for an arbitrary binary operation. In 2006, Geoghegan and Guzmán proved that a group G is solvable if and only if the commutator operation in G eventually satisfies ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1973
ISSN: 0004-9735
DOI: 10.1017/s144678870001421x