# Hochschild and block cohomology varieties are isomorphic

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Let G be a finite group isomorphic to A6 or L3(2) and H be a finite group such that the commuting involution graph of G is isomorphic to the commuting involution graph of H. In this paper we show that if H is generated by its involutions, then G â‰…H.

- Finite groups with S-supplemented p-subgroups. Yang, N.; Guo, W.; Shemetkova, O. // Siberian Mathematical Journal;Mar2012, Vol. 53 Issue 2, p371
Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and Bâˆ© T â‰¤ B. A...

- Approximation properties and linearity of groups. Bryukhanov, O. // Journal of Mathematical Sciences;Jan2013, Vol. 188 Issue 4, p354
We present sufficient conditions for an isomorphic representation over a field of a group by matrices. A criterion of the matrix representation for finitely generated groups is given. Bibliography: 7 titles.

- Recognition by spectrum for simple classical groups in characteristic 2. Vasil'ev, A.; Grechkoseeva, M. // Siberian Mathematical Journal;Nov2015, Vol. 56 Issue 6, p1009
A finite group G is said to be recognizable by spectrum if every finite group with the same set of element orders as G is isomorphic to G. We prove that all finite simple symplectic and orthogonal groups over fields of characteristic 2, except S( q), S(2), O (2), and S( q), are recognizable by...

- Hochschild cohomology for self-injective algebras of tree class D n . I. Volkov, Yu.; Generalov, A. // Journal of Mathematical Sciences;Dec2007, Vol. 147 Issue 5, p7042
The minimal projective bimodule resolution is constructed for algebras in a family of self-injective algebras of finite representation type with tree class Dn. Using this resolution, we calculate the dimensions of the Hochschild cohomology groups for the algebras under consideration. The...

- Representations of a Noncommutative Associative Algebra Related to Quantum Torus of Rank Three. Lin, Shang; Xin, Bin // Acta Mathematica Sinica;Dec2005, Vol. 21 Issue 6, p1521
In this paper, we present some modules over the rankâ€“three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.

- Quantum Weyl reciprocity for cohomology. Brian J. Parshall; Leonard L. Scott // Proceedings of the London Mathematical Society;May2005, Vol. 90 Issue 3, p655
We study the relationship between the cohomology of $q$-Schur algebras and Hecke algebras in type $A$. A key tool, which has independent interest, involves a specific Hecke algebra resolution, introduced in a special case by Deodhar. This resolution is somewhat akin to the Koszul resolution for...

- On Self-Contragredient Genera Of Z[G]-Lattices. Neiße, Olaf; Weiss, Alfred // Bulletin of the London Mathematical Society;Apr2003, Vol. 35 Issue 2, p203
If G is a finite group and V is a finite-dimensional Q[G]-module, V is isomorphic to its contragredient module V*. In general, V need not contain any Z[G]-lattice which is locally isomorphic to its contragredient lattice. Nevertheless, it turns out that for every V there exists another...

- A reduction theorem for the McKay conjecture. Isaacs, I.M.; Malle, Gunter; Navarro, Gabriel // Inventiones Mathematicae;Aug2007, Vol. 170 Issue 1, p33
The McKay conjecture asserts that for every finite group G and every prime p, the number of irreducible characters of G having pï¿½-degree is equal to the number of such characters of the normalizer of a Sylow p-subgroup of G. Although this has been confirmed for large numbers of groups,...