Dual Ore's theorem for distributive intervals of small index
Sebastien Palcoux
TL;DR
This paper extends Ore's theorem to certain distributive and boolean intervals in finite groups, providing new insights with applications to representation theory for groups of specific sizes.
Contribution
It introduces a dual version of Ore's theorem applicable to small index distributive intervals and boolean intervals, expanding theoretical understanding.
Findings
Proves dual Ore's theorem for index <9720
Establishes results for boolean intervals of rank <7
Links findings to representation theory applications
Abstract
This paper proves a dual version of a theorem of Oystein Ore for every distributive interval of finite groups [H,G] of index |G:H|<9720, and for every boolean interval of rank <7. It has applications to representation theory for every finite group.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Algebraic structures and combinatorial models