1 citations · 1 across the 12 of their papers we have counts for
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On the order of a finite group with trivial centre and bounded conjugacy classes
Ilya Gorshkov
A group is called an -$\bfc$-group if each of its conjugacy classes is finite and contains at most elements. By a theorem of B.~H.~Neumann the derived subgroup of such a gro…
Axial Algebras: Questions and Conjectures
I. Gorshkov, S. Shpectorov
Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead…
Characterization of the alternating and symmetric groups by the order and conjugacy class sizes
Ilya Gorshkov, Andrey V. Vasil'ev
We prove that an arbitrary finite group having the same order and same set of conjugacy class sizes as an alternating or symmetric group must be isomorphic to . From thi…
On {2,3,5}-groups with conjugacy classes of distinct sizes
Wei Zhou, Ilya Gorshkov
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct sizes. In this paper, we show that if G is an ah-group and π(G) \subseteq {2,3,5}, w…
Groups of generalized Moufang type and -graded algebras
Ilya Gorshkov
A pair is called a faithful odd transposition group if is a normal set of involutions generating the group and the product of any two distinct elements of has o…