5 citations · 6 across the 11 of their papers we have counts for
14 papers
The problem of recognition of finite simple groups by element orders is solved
Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev
For a finite group , let be the set of element orders of and let be the number of pairwise nonisomorphic finite groups with . We say that the re…
Minimal Polynomials in Spin Representations of Symmetric and Alternating Groups
Amritanshu Prasad, Velmurugan S, Alexey Staroletov
We determine the minimal polynomial of each element of the double cover of the symmetric or alternating group in every irreducible spin representation of .
On eigenvalues of permutations in irreducible representations of symmetric and alternating groups
Alexey Staroletov
Denote the symmetric group of degree by . Let be an irreducible representation of over the field of complex numbers and . In this paper, we describe th…
Solid subalgebras in algebras of Jordan type half
I. Gorshkov, S. Shpectorov, A. Staroletov
The class of algebras of Jordan type was introduced by Hall, Rehren and Shpectorov in 2015 within the much broader class of axial algebras. Algebras of Jordan type are commutat…
Axial view on pseudo-composition algebras and train algebras of rank 3
Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov
We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompos…
On Jordan algebras that are factors of Matsuo algebras
Ilya Gorshkov, Andrey Mamontov, Alexey Staroletov
We describe all finite connected 3-transposition groups whose Matsuo algebras have nontrivial factors that are Jordan algebras. As a corollary, we show that if F is a field of char…
On characterization by Gruenberg-Kegel graph of finite simple exceptional groups of Lie type
Natalia V. Maslova, Viktor V. Panshin, Alexey M. Staroletov
The Gruenberg-Kegel graph of a finite group is the graph whose vertex set is the set of prime divisors of and in which two distinct vertices and are adjace…
Axial algebras of Monster type for diagrams. I
Andrey Mamontov, Alexey Staroletov
Axial algebras are a class of commutative algebras generated by idempotents, with adjoint action semisimple and satisfying a prescribed fusion law. Axial algebras were introduced b…
On recognition of direct powers of finite simple linear groups by spectrum
N. Yang, I. B. Gorshkov, A. M. Staroletov +1
The spectrum of a finite group is the set of its element orders. We give an affirmative answer to Problem 20.58(a) from the Kourovka Notebook proving that for every positive intege…
On primitive -generated axial algebras of Jordan type
Ilya Gorshkov, Alexey Staroletov
Axial algebras of Jordan type are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing , where $η\not\in\{0,1…
Double axes and subalgebras of Monster type in Matsuo algebras
Alexey Galt, Vijay Joshi, Andrey Mamontov +2
Axial algebras are a class of commutative non-associative algebras generated by idempotents, called axes, with adjoint action semi-simple and satisfying a prescribed fusion law. Ax…
The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups
Nanying Yang, Alexey Staroletov
Denote the alternating and symmetric groups of degree by and respectively. Consider a permutation all of whose nontrivial cycles are of the same length.…
Minimal 3-generated Majorana algebras
Andrey Mamontov, Alexey Staroletov, Madeleine Whybrow
Majorana theory was introduced by A. A. Ivanov as the axiomatization of certain properties of the 2A-axes of the Griess algebra. Since its inception, Majorana theory has proved to…
On groups having the prime graph as alternating and symmetric groups
Ilya Gorshkov, Alexey Staroletov
The {\it prime graph} of a finite group is the graph whose vertex set is the set of prime divisors of and in which two distinct vertices and are adjacent i…