metabelian group oor Sjinees
metabelian group
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group G with abelian normal subgroup N and abelian quotient group G/N (equivalently: group with abelian commutator subgroup)
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If F is a finite field with q elements, this metabelian group is of order q(q − 1).
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At first, Skopin considered the case of metabelian groups with two generators with exponents 8, 9, or 27 ( , ).
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After completing work on metabelian groups, Skopin decided to carry out similar calculations on more extended classes of Burnside groups, called by him in transmetabelian groups of type I and II.
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Kaluznin's other significant contributions to group theory include his work on stable automorphism groups, the structure of the variety of n-abelian groups, a classification of metabelian groups, work on locally normal groups of higher categories, and characterisations of the maximal subgroups of the symmetric and alternating groups.
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