A. Zavarnitsine

activity

20072026

most citedFinite simple groups with narrow prime spectrum

107 citations · 164 across the 23 of their papers we have counts for

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27 papers · 1 filter

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 $α_{S} (x)$ 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…

math.GR2024

Generation by conjugate elements of finite almost simple groups with a sporadic socle

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 $α_{S} (x)$ does not exceed a natural number $m$ if some $m…

math.GR2022★ 1 cited

On generations by conjugate elements in almost simple groups with socle $\mbox{}^2F_4(q^2)'$

Danila O. Revin, Andrei V. Zavarnitsine

We prove that if $L=\mbox{}^2F_4(2^{2n+1})'$ and $x$ is a nonidentity automorphism of $L$ then $G = ⟨ L, x ⟩$ has four elements conjugate to $x$ that generate $G$ . This res…

math.GR2022

Automorphisms of nonsplit coverings of $P S L_{2} (q)$ in odd characteristic dividing $q - 1$

Andrei V. Zavarnitsine

We classify the nonsplit extensions of elementary abelian $p$ -groups by $P S L_{2} (q)$ , with odd $p$ dividing $q - 1$ , for an irreducible induced action, calculate the relevant low-dimen…

math.GR2021

Representations and characters of finite groups

D. O. Revin, A. V. Zavarnitsine

This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and pos…

math.GR2021★ 2 cited

Automorphisms of nonsplit extensions of 2-groups by $P S L_{2} (q)$

Danila O. Revin, Andrei V. Zavarnitsine

We complete the description of automorphism groups of all nonsplit extensions of elementary abelian $2$ -groups by $P S L_{2} (q)$ , with $q$ odd, for an irreducible induced action. An ap…

math.GR2020★ 3 cited

The behavior of $π$ -submaximal subgroups under homomorphisms with $π$ -separable kernels

Danila O. Revin, Andrei V. Zavarnitsine

We explore the extent to which constructing the inductive theory of $X$ -submaximal subgroups is possible. To this end, we study the behavior of $π$ -submaximal subgroups…

math.GR2019★ 4 cited

On the behavior of $π$ -submaximal subgroups under homomorphisms

Danila O. Revin, Andrei V. Zavarnitsine

We construct examples that show the difference in behavior or $π$ -maximal and $π$ -submaximal subgroups under group homomorphisms.

math.GR2019★ 2 cited

On the maximal tori in finite linear and unitary groups

Andrei V. Zavarnitsine

To follow up on the results of [1], we propose a computationally efficient explicit cyclic decomposition of the maximal tori in the groups $S L_{n} (q)$ and $S U_{n} (q)$ and their project…

math.GR2017★ 4 cited

On the commutative center of Moufang loops

Alexander N. Grishkov, Andrei V. Zavarnitsine

We construct two infinite series of Moufang loops of exponent $3$ whose commutative center (i.e. the set of elements that commute with all elements of the loop) is not a normal sub…

math.GR2017

Subextensions for co-induced modules

Andrei V. Zavarnitsine

Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some…

math.GR2016

On the embedding of central extensions into wreath products

Andrei V. Zavarnitsine

We find a necessary condition for the embedding of a central extension of a group $G$ with elementary abelian kernel into the wreath product that corresponds to a permutation actio…

math.GR2016

Embedding central extensions of simple linear groups into wreath products

Andrei V. Zavarnitsine

We find a criterion for the embedding of a nonsplit central extension of $P S L_{n} (q)$ with kernel of prime order into the permutation wreath product that corresponds to the action on…

math.GR2015

A Moufang loop with exceptional properties of associators

Ilya B. Gorshkov, Alexandre N. Grichkov, Andrei V. Zavarnitsine

We construct a Moufang loop $M$ of order $3^{19}$ and a pair $a, b$ of its elements such that the set of all elements of $M$ that associate with $a$ and $b$ does not form a subloop.…

math.GR2015★ 3 cited

Multiplication formulas in Moufang loops

Alexander N. Grishkov, Andrei V. Zavarnitsine

Using groups with triality we obtain some general multiplication formulas in Moufang loops, construct Moufang extensions of abelian groups, and describe the structure of minimal ex…

math.GR2014

The structure of maximal tori in spin groups of type $D_{l}$

Andrei V. Zavarnitsine

We determine the abelian invariants of the maximal tori in the finite spin groups of type $D_{l}$

math.GR2014

On a finite 2,3-generated group of period 12

Andrei V. Zavarnitsine

Using calculations in computer algebra systems along with some theoretic results, we construct the largest finite group of period 12 generated by an element of order 2 and an eleme…

math.GR2013★ 4 cited

Subextensions for a permutation PSL(2,q)-module

Andrei Zavarnitsine

Using cohomological methods, we prove the existence of a subgroup isomorphic to SL(2,q), q = -1 (mod 4), in the permutation module for PSL(2,q) in characteristic 2 that arises from…

math.GR2012★ 6 cited

Abelian-by-cyclic Moufang loops

Alexander N. Grishkov, Andrei V. Zavarnitsine

We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient…

math.GR2009

A solvable group isospectral to S(4,3)

Andrei V. Zavarnitsine

We construct a solvable group G of order 5648590729620 such that the set of element orders of G coincides with that of the simple group S(4,3). This completes the determination of…

Simple groups with narrow prime spectrum: Extended list

Refined conjugate generation in sporadic groups

On generation by triality automorphisms

Conjugate generation of sporadic almost simple groups

Explicit inverse Shapiro isomorphism and its application

Generation by conjugate elements of finite almost simple groups with a sporadic socle

On generations by conjugate elements in almost simple groups with socle $\mbox{}^2F_4(q^2)'$

Automorphisms of nonsplit coverings of PSL2​(q) in odd characteristic dividing q−1

Representations and characters of finite groups

Automorphisms of nonsplit extensions of 2-groups by PSL2​(q)

The behavior of π-submaximal subgroups under homomorphisms with π-separable kernels

On the behavior of π-submaximal subgroups under homomorphisms

On the maximal tori in finite linear and unitary groups

On the commutative center of Moufang loops

Subextensions for co-induced modules

On the embedding of central extensions into wreath products

Embedding central extensions of simple linear groups into wreath products

A Moufang loop with exceptional properties of associators

Multiplication formulas in Moufang loops

The structure of maximal tori in spin groups of type Dl​

On a finite 2,3-generated group of period 12

Subextensions for a permutation PSL(2,q)-module

Abelian-by-cyclic Moufang loops

A solvable group isospectral to S(4,3)

Automorphisms of nonsplit coverings of $P S L_{2} (q)$ in odd characteristic dividing $q - 1$

Automorphisms of nonsplit extensions of 2-groups by $P S L_{2} (q)$

The behavior of $π$ -submaximal subgroups under homomorphisms with $π$ -separable kernels

On the behavior of $π$ -submaximal subgroups under homomorphisms

The structure of maximal tori in spin groups of type $D_{l}$