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篇目详细内容 |
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【篇名】 |
OD-Characterization of alternating and symmetric groups of degrees 16 and 22 |
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【刊名】 |
Frontiers of Mathematics in China |
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【刊名缩写】 |
Front. Math. China |
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【ISSN】 |
1673-3452 |
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【EISSN】 |
1673-3576 |
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【DOI】 |
10.1007/s11464-009-0037-1 |
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【出版社】 |
Higher Education Press and Springer-Verlag |
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【出版年】 |
2009 |
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【卷期】 |
4
卷4期 |
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【页码】 |
669-680
页,共
12
页 |
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【作者】 |
A. R. MOGHADDAMFAR;
A. R. ZOKAYI;
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【关键词】 |
OD-characterizability of a finite group; degree pattern; prime graph |
【摘要】 |
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Let G be a finite group and π(G) be the set of all prime divisors of its order. The prime graph GK(G) of G is a simple graph with vertex set π(G), and two distinct primes p, q ∈ π(G) are adjacent by an edge if and only if G has an element of order pq. For a vertex p ∈ π(G), the degree of p is denoted by deg(p) and as usual is the number of distinct vertices joined to p. If π(G) = {p1, p2, …, pk}, where p1<p2<…<pk, then the degree pattern of G is defined by D(G) = (deg(p1), deg(p2), … , deg(pk)). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions |H| = |G| and D(H) = D(G). In addition, a 1-fold Odcharacterizable group is simply called OD-characterizable. In the present article, we show that the alternating group A22 is OD-characterizable. We also show that the automorphism groups of the alternating groups A16 and A22, i.e., the symmetric groups S16 and S22 are 3-fold OD-characterizable. It is worth mentioning that the prime graph associated to all these groups are connected. |
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