Sums of prime element orders in finite groups
نویسندگان
چکیده
منابع مشابه
The Number of Finite Groups Whose Element Orders is Given
The spectrum ω(G) of a finite group G is the set of element orders of G. If Ω is a non-empty subset of the set of natural numbers, h(Ω) stands for the number of isomorphism classes of finite groups G with ω(G) = Ω and put h(G) = h(ω(G)). We say that G is recognizable (by spectrum ω(G)) if h(G) = 1. The group G is almost recognizable (resp. nonrecognizable) if 1 < h(G) < ∞ (resp. h(G) = ∞). In t...
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There are several graphs associated with finite groups which are currently of interest in the field. This subject of this project are graphs related to the element orders of a finite group. The best known such graph is the prime graph Γ(G) of the group G and is defined as follows. The vertices are the prime numbers dividing the order (=number of elements) of the group, and two such primes are l...
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We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if t is an integer different from 0, 1 or −1 and if A ⊂ Z/pZ is not too large (with respect to p), then |A+t·A| > (2+θt)|A|−w(t) for some constant w(t) depending only on t and for some explicit real number θt > 0 (except in the case |t| = 3). In the important case |t| = 2,...
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ژورنال
عنوان ژورنال: Journal of Taibah University for Science
سال: 2018
ISSN: 1658-3655
DOI: 10.1080/16583655.2018.1468398