相关论文: Large characteristic subgroups of surface groups n…

We notice that the class of nontrivial groups without proper subgroups of finite index is not elementary, because some groups in this class, such as $\mathbb Q*\mathbb Q$, have ultrapowers that map homomorphically onto $\mathbb Z/p\mathbb…

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We have sorted the SmallGroups library of all the finite groups of order smaller than 2000 to identify the groups that possess a faithful three-dimensional irreducible representation (`irrep') and cannot be written as the direct product of…

We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.

We classify Coble surfaces with finite automorphism group in arbitrary characteristic not equal to 2. There are exactly 9 isomorphism classes of such surfaces.

We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group.

A loop is (right) automorphic if all its (right) inner mappings are automorphisms. Using the classification of primitive groups of small degrees, we show that there is no nonassociative simple commutative automorphic loop of order less than…

This paper reproduces the text of a part of the Author's DPhil thesis. It gives a proof of the classification of non-trivial, finite homogeneous geometries of sufficiently high dimension which does not depend on the classification of the…

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…

We determine an upper bound for the size of a stem $p$-group in terms of its breadth and its maximum character degree.

This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite $p$-groups with the smallest maximum size for neighborhoods of…

For a finite group $G$, we define the inclusion graph of subgroups of $G$, denoted by $\mathcal I(G)$, is a graph having all the proper subgroups of $G$ as its vertices and two distinct vertices $H$ and $K$ in $\mathcal I(G)$ are adjacent…

A proof of freeness of the commutator subgroup of the fundamental group of a smooth irreducible affine curve over a countable algebraically closed field of nonzero characteristic. A description of the abelianizations of the fundamental…

We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.

We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.

Motivated by the Problem $164$ proposed by Y. Berkovich and E. Zhmud' in their book "Characters of finite groups, Part $1$", we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based…

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

We prove that the mapping class group of a closed oriented surface of genus $\rho \ge 3$ has no proper subgroup of index $\le 4 \rho +4$.

We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a…