منابع مشابه
Groups - Additive Notation
We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset ...
متن کاملAdditive Bases in Groups
We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.
متن کاملThe Orbifold Notation for Two-Dimensional Groups
The finite subgroups of the three-dimensional (3-D) orthogonal group have been enumerated by several authors, using several different methods (see [3]). The 17 plane crystallographic groups have also been enumerated by Polya and Niggli, who used a distinct method analogous to that used 30 years earlier for the harder problem of enumerating the 219 space groups. The aim of this paper is to descr...
متن کاملAdditive Bases in Abelian Groups
Let G be a finite, non-trivial abelian group of exponent m, and suppose that B1, . . . , Bk are generating subsets of G. We prove that if k > 2m ln log2 |G|, then the multiset union B1 ∪ · · · ∪ Bk forms an additive basis of G; that is, for every g ∈ G there exist A1 ⊆ B1, . . . , Ak ⊆ Bk such that g = ∑k i=1 ∑ a∈Ai a. This generalizes a result of Alon, Linial, and Meshulam on the additive base...
متن کاملIsometry Groups of Additive Codes
When C ⊆ F is a linear code over a finite field F, every linear Hamming isometry of C to itself is the restriction of a linear Hamming isometry of F to itself, i.e., a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping C to itself is an additive Hamming isometry, but there exist additive Hamming isometries that are...
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: Formalized Mathematics
سال: 2015
ISSN: 1898-9934
DOI: 10.1515/forma-2015-0013