A presentation and a representation of the Held group

1996 ◽  
Vol 66 (4) ◽  
pp. 265-275 ◽  
Author(s):  
Jörg Hrabě de Angelis
Keyword(s):  
Held Group

A New Uniqueness Proof for the Held Group

1991 ◽  
Vol 23 (3) ◽  
pp. 235-238 ◽  
Author(s):  
Leonard H. Soicher
Keyword(s):  
Uniqueness Proof ◽  
Held Group

scholarly journals Broué's abelian defect group conjecture for the Held group and the sporadic Suzuki group

2004 ◽  
Vol 279 (2) ◽  
pp. 638-666 ◽  
Author(s):  
Shigeo Koshitani ◽  
Naoko Kunugi ◽  
Katsushi Waki
Keyword(s):  
Defect Group ◽  
Suzuki Group ◽  
Held Group

Ambivalently held group-optimizing predispositions

1994 ◽  
Vol 17 (4) ◽  
pp. 614-614 ◽  
Author(s):  
Donald T. Campbell ◽  
John B. Gatewood
Keyword(s):  
Held Group

scholarly journals Calculation of the 7-modular characters of the Held group

1988 ◽  
Vol 117 (1) ◽  
pp. 240-255 ◽  
Author(s):  
A.J.E Ryba
Keyword(s):  
Held Group

scholarly journals The Alperin and Dade Conjectures for the Simple Held Group

1997 ◽  
Vol 189 (1) ◽  
pp. 34-57 ◽  
Author(s):  
Jianbei An
Keyword(s):  
Held Group

scholarly journals The evolution of strongly-held group identities through agent-based cooperation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Roger M. Whitaker ◽  
Gualtiero B. Colombo ◽  
Yarrow Dunham
Keyword(s):  
Indirect Reciprocity ◽  
Agent Based ◽  
Individual Level ◽  
The Social ◽  
Identity Fusion ◽  
Agent Interaction ◽  
Group Identities ◽  
Psychology Literature ◽  
Collective Benefit ◽  
Held Group

AbstractIdentity fusion represents a strongly-held personal identity that significantly overlaps with that of a group, and is the current best explanation as to why individuals become empowered to act with extreme self-sacrifice for a group of non-kin. This is widely seen and documented, yet how identity fusion is promoted by evolution is not well-understood, being seemingly counter to the selfish pursuit of survival. In this paper we extend agent-based modelling to explore how and why identity fusion can establish itself in an unrelated population with no previous shared experiences. Using indirect reciprocity to provide a framework for agent interaction, we enable agents to express their identity fusion towards a group, and observe the effects of potential behaviours that are incentivised by a heightened fusion level. These build on the social psychology literature and involve heightened sensitivity of fused individuals to perceived hypocritical group support from others. We find that simple self-referential judgement and ignorance of perceived hypocrites is sufficient to promote identity fusion and this is easily triggered by a sub-group of the population. Interestingly the self-referential judgement that we impose is an individual-level behaviour with no direct collective benefit shared by the population. The study provides clues, beyond qualitative and observational studies, as to how hypocrisy may have established itself to reinforce the collective benefit of a fused group identity. It also provides an alternative perspective on the controversial proposition of group selection - showing how fluidity between an individual’s reputation and that of a group may function and influence selection as a consequence of identity fusion.

The Fischer–Clifford Matrices of a Maximal Subgroup of the Sporadic Simple Group of Held

2007 ◽  
Vol 14 (01) ◽  
pp. 135-142 ◽  
Author(s):  
Faryad Ali
Keyword(s):  
Simple Group ◽  
Computer Algebra ◽  
Local Structure ◽  
Computer Algebra System ◽  
Conjugacy Classes ◽  
Character Table ◽  
Maximal Subgroups ◽  
Split Extension ◽  
Sporadic Simple Group ◽  
Held Group

The Held group He discovered by Held [10] is a sporadic simple group of order 4030387200 = 210.33.52.73.17. The group He has 11 conjugacy classes of maximal subgroups as determined by Butler [5] and listed in the 𝔸𝕋𝕃𝔸𝕊. Held himself determined much of the local structure of He as well as the conjugacy classes of its elements. Thompson calculated the character table of He . In the present paper, we determine the Fischer–Clifford matrices and hence compute the character table of the non-split extension 3·S7, which is a maximal subgroups of He of index 226560 using the technique of Fischer–Clifford matrices. Most of the computations were carried out with the aid of the computer algebra system 𝔾𝔸ℙ.

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