Related papers: A note on noninner automorphisms of order $p$ for …

We present a structural description of finite nilpotent groups of class at most $2$ using a specified number of subdirect and central products of $2$-generated such groups. As a corollary, we show that all of these groups are isomorphic to…

The largest prime p that can be the order of an automorphism of a 2-(35,17,8) design is p=17, and all 2-(35,17,8) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2-(35,17,8) designs with automorphisms of…

In this paper, we construct an infinite families of group $G$ of order $4p^m$ which can be an automorphism group of some regular polytope with type $\{p, 2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are the…

Results of the computation of the automorphism groups for the groups of orders $16p$ and $16p^{2}$ are given. In some cases it has not been possible to give as complete a set of results as was done previously for the case of groups of order…

Suppose that a finite $p$-group $P$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ that is a cyclic $p$-group and with complement $H$. It is proved that if the fixed-point subgroup $C_P(H)$ of the complement is nilpotent of…

A presentation as well as a structural description of the automorphism group of a family of 3-generator finite $p$-groups is given, $p$ being an odd prime.

We prove that the degree $r(2p-3)$ cohomology of any finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a simple…

Let p be an odd prime number. We show that there exists a finite group of order p^{p+3} whose the mod p cycle map from the mod p Chow ring of its classifying space to its ordinary mod p cohomology is not injective.

A p-local finite group is an algebraic structure with a classifying space which has many of the properties of p-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic…

We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…

Among the simplest invariants of the sporadic finite simple groups are their outer automorphism groups. For 12 of the 26 possible isomorphism types of a sporadic simple group G, the outer automorphism group Out(G) has order 2, and in the…

An irreducible, algebraic curve $\mathcal X_g$ of genus $g\geq 2$ defined over an algebraically closed field $k$ of characteristic $\mbox{char } \, k = p \geq 0$, has finite automorphism group $\mbox{Aut} (\mathcal X_g)$. In this paper we…

In this paper we prove that every automorphism of a Chevalley group with the root system G_2 over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.

The so-called Tits class, associated to an adjoint absolutely almost simple algebraic group, provides a cohomological obstruction for this group to admit an outer automorphism. If the group has inner type, this obstruction is the only one.…

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly $p^m$ fixed points such that $\phi^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with…

Let $p$ be an odd prime number. In this paper, we characterize the nonabelian composition factors of a finite group with odd $p$-Sylow automizers, and then prove that the McKay conjecture, the Alperin weight conjecture and the Alperin-McKay…

For each prime $p$ we construct a family $\{G_i\}$ of finite $p$-groups such that $|\Aut (G_i)|/|G_i|$ goes to $0$, as $i$ goes to infinity. This disproves a well-known conjecture that $|G|$ divides $|\Aut(G)|$ for every non-abelian finite…

We show the existence of some non-classical cohomological p-adic automorphic eigenforms for SL(2) using endoscopy and the geometry of eigenvarieties. These forms seem to account for some non-automorphic members of classical global…

We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also classify finite $p$-groups and finite simple groups with…

We prove that the degree $r(2p-3)$ cohomology of any (untwisted) finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a…