Word length in surface groups with characteristic generating sets
نویسندگان
چکیده
منابع مشابه
Generating Sets of Mathieu Groups
Julius Whiston [6] calculated the maximum size of an irredundant generating set for Sn and An by examination of maximal subgroups. Using analogous considerations, we will compute upper bounds to this value for the first two Mathieu groups, M11 and M12. Computational results gave explicit irredundant generating sets of M11 and M12 of size 5 and 6, respectively. Together these give the full resul...
متن کاملIrredundant Generating Sets of Finite Nilpotent Groups
It is a standard fact of linear algebra that all bases of a vector space have the same cardinality, namely the dimension of the vector space over its base field. If we treat a vector space as an additive abelian group, then this is equivalent to saying that an irredundant generating set for a vector space must have cardinality equal to the dimension of the vector space. The same is not true for...
متن کاملOn sampling generating sets of finite groups
The problem of determining the structure of Nk(G) is of interest in several contexts. The counting problem goes back to Philip Hall, who expressed Nk(G) as a Möbius type summation of Nk(H) over all maximal subgroups H ⊂ G (see [23]). Recently the counting problem has been studied for large simple groups where remarkable progress has been made (see [25, 27]). In this paper we analyze Nk for solv...
متن کاملProperties of Generating Sets of Finite Groups
Students in the project should have a solid background in basic linear algebra and abstract algebra. For example, the first six chapters of the textbook by Dummit and Foote, Abstract Algebra, 3rd edition, Wiley, would be more than adequate for the required background in group theory. For example, section 5.2 defines the term elementary divisors which appears below and in one standard descriptio...
متن کاملProperties of Generating Sets of Finite Groups
Students in the project should have a solid background in basic linear algebra and abstract algebra. For example, the first six chapters of the textbook by Dummit and Foote, Abstract Algebra, 3rd edition, Wiley, would be more than adequate for the required background in group theory. For example, section 5.2 defines the term elementary divisors which appears below and in one standard descriptio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09443-4