| Autor: |
Azad, Azizollah, Britnell, John R., Gill, Nick |
| Předmět: |
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| Zdroj: |
Forum Mathematicum; Nov2015, Vol. 27 Issue 6, p3745-3782, 38p |
| Abstrakt: |
Let G be a finite group and c be an element of . A subgroup H of G is said to be c-nilpotent if it is nilpotent and has nilpotency class at most c. A subset X of G is said to be non- c-nilpotent if it contains no two elements x and y such that the subgroup is c-nilpotent. In this paper we study the quantity , defined to be the size of the largest non- c-nilpotent subset of L. In the case that L is a finite group of Lie type, we identify covers of L by c-nilpotent subgroups, and we use these covers to construct large non- c-nilpotent sets in the group L. We prove that for groups L of fixed rank r, there exist constants Dr and Er such that , where N is the number of maximal tori in L. In the case of groups L with twisted rank 1, we provide exact formulae for for all . If we write q for the level of the Frobenius endomorphism associated with L and assume that q > 5, then may be expressed as a polynomial in q with coefficients in . [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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