منابع مشابه
Action of a Frobenius-like group with kernel having central derived subgroup
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h ∈ H. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with [F ′, H] = 1. In case where CG(F ) = 1 we prove that the groups G and CG(H) have the same nilpotent length un...
متن کاملAction of a Frobenius-like group with fixed-point free kernel
We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that ŒF; h D F for all nonidentity elements h 2 H . We prove that any irreducible nontrivial FH -module for a Frobeniuslike group FH of odd order over an algebraically-closed field has an H -regular direct summand if either F is fixed-point free on V or F acts nont...
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In this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a nonabelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1463 non-isomorphic designs. The orders of the full automorphism groups of these designs all...
متن کاملFROBENIUS n-GROUP ALGEBRAS
Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66–67).
متن کاملFROBENIUS ACTION ON l-ADIC ORBIFOLD COHOMOLOGY
We extend the definition of orbifold (Chen-Ruan) cohomology to tame Deligne-Mumford stacks over fields of positive characteristic and prove that a modified version of the Frobenius action preserves the product. We conjecture a relationship between the arithmetic information contained by this action and the zeta function of a crepant resolution of the coarse moduli space (when each exist).
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.01.005