1,226 research outputs found
Morita equivalence classes of 2-blocks of defect three
We give a complete description of the Morita equivalence classes of blocks
with elementary abelian defect groups of order 8 and of the derived
equivalences between them. A consequence is the verification of Brou\'e's
abelian defect group conjecture for these blocks. It also completes the
classification of Morita and derived equivalence classes of 2-blocks of defect
at most three defined over a suitable field
Classifying blocks with abelian defect groups of rank for the prime
In this paper we classify all blocks with defect group up to Morita equivalence. Together with a recent paper of Wu,
Zhang and Zhou, this completes the classification of Morita equivalence classes
of -blocks with abelian defect groups of rank at most . The
classification holds for blocks over a suitable discrete valuation ring as well
as for those over an algebraically closed field. The case considered in this
paper is significant because it involves comparison of Morita equivalence
classes between a group and a normal subgroup of index , so requires novel
reduction techniques which we hope will be of wider interest. We note that this
also completes the classification of blocks with abelian defect groups of order
dividing up to Morita equivalence. A consequence is that Broue's abelian
defect group conjecture holds for all blocks mentioned above
Towards Donovan's conjecture for abelian defect groups
We define a new invariant for a -block, the strong Frobenius number, which
we use to address the problem of reducing Donovan's conjecture to normal
subgroups of index p. As an application we use the strong Frobenius number to
complete the proof of Donovan's conjecture for 2-blocks with abelian defect
groups of rank at most 4 and for 2-blocks with abelian defect groups of order
at most 64
Some examples of Picard groups of blocks
We calculate examples of Picard groups for 2-blocks with abelian defect
groups with respect to a complete discrete valuation ring. These include all
blocks with abelian 2-groups of 2-rank at most three with the exception of the
principal block of J1. In particular this shows directly that all such Picard
groups are finite and Picent, the group of Morita auto-equivalences fixing the
centre, is trivial. These are amongst the first calculations of this kind.
Further we prove some general results concerning Picard groups of blocks with
normal defect groups as well as some other cases.Comment: 21 page
Rings whose multiples are direct summands
We give a reduction to quasisimple groups for Donovan’s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring O . Consequences are that Donovan’s conjecture holds for O -blocks with abelian defect groups for the prime two, and that, using recent work of Farrell and Kessar, for arbitrary primes Donovan’s conjecture for O -blocks with abelian defect groups reduces to bounding the Cartan invariants of blocks of quasisimple groups in terms of the defect. A result of independent interest is that in general (i.e. for arbitrary defect groups) Donovan’s conjecture for O -blocks is a consequence of conjectures predicting bounds on the O -Frobenius number and on the Cartan invariants, as was proved by Kessar for blocks defined over an algebraically closed field
Underreporting Chargeable Time: A Continuing Problem for Public Accounting Firms
Prior research shows that underreporting chargeable time has been a concern for public accounting firms even though many of these firms have policies and procedures that prohibit eating time. The purpose of this study is to examine the current state of this problem and to provide recommendations to manage the problem more effectively. Practicing public accountants at all professional levels were surveyed to determine the extent, opportunity, ethical perception and perceived benefits of underreporting time. The results show that although the majority of the respondents believe underreporting time is unethical, the majority of them did not report all of their chargeable hours in the prior year. The main reasons for such behavior stem from the desire to: (1) receive better periodic performance evaluations, (2) be viewed as competent by superiors and (3) receive promotions
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