منابع مشابه
On automorphisms of extremal even unimodular lattices
The automorphism groups of the three known extremal even unimodular lattices of dimension 48 and the one of dimension 72 are determined using the classification of finite simple groups. Restrictions on the possible automorphisms of 48-dimensional extremal lattices are obtained. We classify all extremal lattices of dimension 48 having an automorphism of order m with φ(m) > 24. In particular the ...
متن کاملOn Marginal Automorphisms of a Group Fixing the Certain Subgroup
Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x ∈ G, x−1α(x) ∈ W∗(G), where W∗(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) ...
متن کاملAutomorphisms of even unimodular lattices and unramified Salem numbers
In this paper we study the characteristic polynomials S(x) = det(xI − F | IIp,q) of automorphisms of even, unimodular lattices with signature (p, q). In particular we show any Salem polynomial of degree 2n satisfying S(−1)S(1) = (−1)n arises from an automorphism of an indefinite lattice, a result with applications to K3 surfaces.
متن کاملAutomorphisms of extremal unimodular lattices in dimension 72
The paper narrows down the possible automorphisms of extremal even unimodular lattices of dimension 72. With extensive computations in Magma using the very sophisticated algorithm for computing class groups of algebraic number fields written by Steve Donnelly it is shown that the extremal even unimodular lattice Γ72 from [17] is the unique extremal even unimodular lattice of dimension 72 that a...
متن کاملOD-characterization of $U_3(9)$ and its group of automorphisms
Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1951
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1951-0043847-x