Geodesic
Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 346-351

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An A-group is a finite solvable group all of whose Sylow subgroups are abelian. In this paper, we are interested in bounding the derived length of an A-group G as a function of the number of distinct sizes of the conjugacy classes of G. Although we do not find a specific bound of this type, we do prove that such a bound exists. We also prove that if G is an A-group with a faithful and completely reducible G-module V, then the derived length of G is bounded by a function of the number of distinct orbit sizes under the action of G on V.
DOI : 10.4153/CMB-1996-041-6
Mots-clés : 20 
Marshall, Mary K. Numbers Of Conjugacy Class Sizes And Derived Lengths for A-Groups. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 346-351. doi: 10.4153/CMB-1996-041-6
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     title = {Numbers {Of} {Conjugacy} {Class} {Sizes} {And} {Derived} {Lengths} for {A-Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {346--351},
     year = {1996},
     volume = {39},
     number = {3},
     doi = {10.4153/CMB-1996-041-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-041-6/}
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