Results 91 to 100 of about 96,321 (254)
Automorphisms and ultraspecial groups
Journal of Algebra, 1979 In [l], we have introduced the classes GCZ( p) and U(p) of semi-extraspecial and ultraspecial p-groups, namely @Z(p) = {X 1 X is a finite p-group, X’ # 1, Nmax Z(X) * X/N is extraspecial} and U(p) = {X j XE EK!!( p), r(X) = *r(X)}. If X is a semi-extraspecial p-group, then X is a special group of even rank with r(X’) C GF(p”)}, (a, b, ~)(a’, b’, c’) =
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On the Automorphism Group of a Lie Group [PDF]
Proceedings of the American Mathematical Society, 1974 It is proved that the automorphism group of a connected real or complex Lie group contains an open real or complex algebraic subgroup. It follows that the identity component of the group of complex automorphisms of a connected complex Lie group is a complex algebraic group.
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Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
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Journal of Combinatorial Designs, Volume 33, Issue 10, Page 379-387, October 2025.ABSTRACT The E ( s 2 )‐optimal and minimax‐optimal supersaturated designs (SSDs) with 12 rows, 11 q columns, and s max = 4 are enumerated in a computer search: there are, respectively, 34, 146, 0, 3, and 1 such designs for q = 2 , 3 , 4 , 5, and 6. Cheng and Tang proved that for q > 6, there are no such SSDs.
Luis B. Morales
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Finite Vertex Bi-Primitive 2-Arc Transitive Graphs Admitting a Two-Dimensional Linear Group
IEEE Access, 2019 A graph is said to be vertex bi-primitive, if it is a bipartite graph, and the setwise stabilizer of its automorphism group acts primitively on two bi-parts.
Xiaohui Hua
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Groups with Anomalous Automorphisms
Journal of Algebra, 1996 Let \(G\) be a group. The set \(\Aut_{nn}G\) of all automorphisms of \(G\) fixing every non-normal subgroup of \(G\) is a normal subgroup of the full automorphism group \(\Aut G\) of \(G\). Of course, \(\Aut_{nn}G\) contains the group \(P\Aut G\) of all power automorphisms of \(G\), and the structure of groups \(G\) such that \(P\Aut G\neq\Aut_{nn}G ...
Rolf Brandl, Libero Verardi
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Symmetric 2‐ ( 35 , 17 , 8 ) Designs With an Automorphism of Order 2
Journal of Combinatorial Designs, Volume 33, Issue 10, Page 399-403, October 2025.ABSTRACT The largest prime p that can be the order of an automorphism of a 2‐ ( 35 , 17 , 8 ) design is p = 17, and all 2‐ ( 35 , 17 , 8 ) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2‐ ( 35 , 17 , 8 ) designs with automorphisms of an odd prime order p < 17 were classified in Bouyukliev, Fack and Winne and ...
Sanja Rukavina, Vladimir D. Tonchev
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On Endomorphism Universality of Sparse Graph Classes
Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
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On Groups of Automorphism of Lie Groups [PDF]
Proceedings of the National Academy of Sciences, 1944 Not ...
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On the implementability of automorphism groups [PDF]
Communications in Mathematical Physics, 1969 LetA be aC*-algebra andG be a locally compact group acting as strongly continuous automorphisms onA. Let π be a representation ofA then we say π is a covariant representation if there exists a strongly continuous unitary representation of the group acting onHπ which implements the automorphisms.
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