Leedham-Green, C. R.; Newman, M. F. (1980), "Space groups and groups of prime-power order. I.", Arch. Math., 35 (3), Basel: 193–202, doi:10.1007/BF01235338, MR 0583590
Leedham-Green, C. R. (1994), "The structure of finite p-groups", J. London Math. Soc., Series 2, 50 (1): 49–67, doi:10.1112/jlms/50.1.49, MR 1277754
Shalev, Aner (1994), "The structure of finite p-groups: effective proof of the coclass conjectures", Invent. Math., 115 (2): 315–345, doi:10.1007/bf01231763, MR 1258908
January 01, 1970
coclass, gamebird, species, koklass, pheasant, mathematics, coclass, finite, group, order, where, class, coclass, conjectures, editthe, coclass, conjectures, were, introduced, leedham, green, newman, 1980, proved, leedham, green, 1994, shalev, 1994, they, conj. For the gamebird species see Koklass pheasant In mathematics the coclass of a finite p group of order pn is n c where c is the class The coclass conjectures editThe coclass conjectures were introduced by Leedham Green and Newman 1980 and proved by Leedham Green 1994 and Shalev 1994 They are Conjecture A Every p group has a normal subgroup of class 2 with index depending only on p and its coclass Conjecture B The solvable length of a p group can be bounded in terms of p and the coclass Conjecture C A pro p group of finite coclass is solvable Conjecture D There are only finitely many pro p groups of given coclass Conjecture E There are only finitely many solvable pro p groups of given coclass See also editDescendant tree group theory References editLeedham Green C R Newman M F 1980 Space groups and groups of prime power order I Arch Math 35 3 Basel 193 202 doi 10 1007 BF01235338 MR 0583590 Leedham Green C R 1994 The structure of finite p groups J London Math Soc Series 2 50 1 49 67 doi 10 1112 jlms 50 1 49 MR 1277754 Shalev Aner 1994 The structure of finite p groups effective proof of the coclass conjectures Invent Math 115 2 315 345 doi 10 1007 bf01231763 MR 1258908 Retrieved from https en wikipedia org w index php title Coclass amp oldid 1204308201, wikipedia, wiki, book, books, library,