A. Zavarnitsine

activity

20242026

collaborators

5 papers

math.GR2026

Simple groups with narrow prime spectrum: Extended list

Andrei V. Zavarnitsine

Generalising a previous result, we determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding $1 0^{4}$ . The computer code for this and similar…

math.GR2026

Refined conjugate generation in sporadic groups

Danila O. Revin, Andrei V. Zavarnitsine

Given an automorphism $x$ of order bigger than $2$ of a sporadic simple group $S$ , we show that there are at most $3$ conjugates of $x$ required to generate a subgroup of order div…

math.GR2025

On generation by triality automorphisms

Danila O. Revin, Andrei V. Zavarnitsine

We clarify the structure of subgroups generated by conjugate graph automorphisms of order $3$ of $O_{8}^{+} (2)$ and $O_{8}^{+} (3)$ . As a result, we obtain a correction to a paper by S. Gue…

math.GR2025

Conjugate generation of sporadic almost simple groups

Danila O. Revin, Andrei V. Zavarnitsine

As defined by Guralnick and Saxl, given a nonabelian simple group $S$ and its nonidentity automorphism $x$ , a natural number $I^\pm_{S} (x)$ is the minimum number of conjugates of $x$ in…

math.GR2024

Explicit inverse Shapiro isomorphism and its application

Andrei V. Zavarnitsine

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a un…