منابع مشابه
On the subgroup permutability degree of some finite simple groups
Consider a finite group G and subgroups H,K of G. We say that H and K permute if HK = KH and call H a permutable subgroup if H permutes with every subgroup of G. A group G is called quasi-Dedekind if all subgroups of G are permutable. We can define, for every finite group G, an arithmetic quantity that measures the probability that two subgroups (chosen uniformly at random with replacement) per...
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Let G be a finitely generated residually finite group and let an(G) denote the number of index n subgroups of G. If an(G) ≤ nα for some α and for all n, then G is said to have polynomial subgroup growth (PSG, for short). The degree of G is then defined by deg(G) = limsup log an(G) log n . Very little seems to be known about the relation between deg(G) and the algebraic structure of G. We derive...
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This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of F× q6 , for q ≡ 1 mod 6. Our result arises from considering the Weil restriction of scalars of this group from Fq6 to Fq2 , and provides efficiency improvements for both pairingbased and torus-based cryptographic protocols. In particular we argue that such fields are ideally suited for the l...
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The theory of linear lattices is presented as a system with multiple-conclusion rules. It is shown through the permutability of the rules that the system enjoys a subterm property: all terms in a derivation can be restricted to terms in the conclusion or in the assumptions. Decidability of derivability with the rules for linear lattices follows through the termination of proof-search.
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This paper describes several speedups for computation in the order p + 1 subgroup of Fp2 and the order p 2 − p + 1 subgroup of Fp6 . These results are in a way complementary to LUC and XTR, where computations in these groups are sped up using trace maps. As a side result, we present an efficient method for XTR with p ≡ 3 mod 4.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2013
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089512000766