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Let G be a finite group and π e (G) be the set of element orders of G. Let k ∈ π e (G) and m k be the number of elements of order k in G. Set nse(G):= {m k : k ∈ π e (G)}. In fact nse(G) is the set of sizes of elements with the same order in G. In this paper, by nse(G) and order, we give a new characterization of finite projective special linear groups L 2(p) over a field with p elements, where p is prime. We prove the following theorem: If G is a group such that |G| = |L 2(p)| and nse(G) consists of 1, p 2 ? 1, p(p + ?)/2 and some numbers divisible by 2p, where p is a prime greater than 3 with p ≡ 1 modulo 4, then G ? L 2(p). 相似文献
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Let G be a finite group. The prime graph ??(G) of G is defined as follows. The vertices of ??(G) are the primes dividing the order of G and two distinct vertices p, p?? are joined by an edge if G has an element of order pp??. Let L=L n (2) or U n (2), where n?R17. We prove that L is quasirecognizable by prime graph, i.e. if G is a finite group such that ??(G)=??(L), then G has a unique nonabelian composition factor isomorphic to L. As a consequence of our result we give a new proof for the recognition by element orders of L n (2). Also we conclude that the simple group U n (2) is quasirecognizable by element orders. 相似文献
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V. P. Burichenko 《Algebra and Logic》2008,47(6):384-394
Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S2(V) be its symmetric square. We construct a 2-cohomology group H2(G, L). The group is one-dimensional over F
q if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H2(G, L) = 0. Previously, such groups H2(G, L) were known for the cases where n = 2 or q = p is prime. We state that H2(G, L) are trivial for n ⩾ 3 and q = pm, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods.
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Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008. 相似文献
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A. K. Shlyopkin 《Algebra and Logic》1998,37(5):345-350
A group G is saturated with groups of the set X if every finite subgroup K≤G is embedded in G into a subgroup L isomorphic
to some group of X. We study periodic conjugate biprimitive finite groups saturated with groups in the set {U3(2n)}. It is proved that every such group is isomorphic to a simple group U3(Q) over a locally finite field Q of characteristic 2.
Supported by the RF State Committee of Higher Education.
Translated fromAlgebra i Logika, Vol. 37, No. 5, pp. 606–615, September–October, 1998. 相似文献
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Nicolas Bougard 《组合设计杂志》2006,14(5):333-350
An (n,k,p,t)‐lotto design is an n‐set N and a set of k‐subsets of N (called blocks) such that for each p‐subset P of N, there is a block for which . The lotto number L(n,k,p,t) is the smallest number of blocks in an (n,k,p,t)‐lotto design. The numbers C(n,k,t) = L(n,k,t,t) are called covering numbers. It is easy to show that, for n ≥ k(p ? 1), For k = 3, we prove that equality holds if one of the following holds:
- (i) n is large, in particular
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- (iii) 2 ≤ p ≤ 6.
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Robert Lee Wilson 《代数通讯》2013,41(4):319-364
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Conditions characterizing Fourier transforms in L2(R) are given. 相似文献
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In this paper, we study certain groupsG generated by two elementsa andb of orders 2 andn respectively subject to one further defining relation, and determine their structure. We also point out certain connections
between these groups and the Fibonacci groupsF(r, n). 相似文献
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G(3, m, n) is the group presented by
. In this paper, we study the structure of G(3, m, n). We also give a new efficient presentation for the Projective Special Linear group PSL(2, 5) and in particular we prove that PSL(2, 5) is isomorphic to G(3, m, n) under certain conditions. 相似文献
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The automorphism groups of the one-factorizations GK(2n,G) are computed. It is shown that every 1-factorization of K2n with a subgroup of the automorphism group that acts sharply 2-transitively on the one-factors must be GK(pm + 1, (Zp)m) for some odd prime p. © 1994 John Wiley & Sons, Inc. 相似文献