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Results tagged with sporadic-groups
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user 22709
A sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. All the other finite simple groups form 18 infinite families numbered by q - power of prime number and n - natural number. Sporadic groups attach attention due to their sporadic/exceptional nature - similar to exceptional Lie groups. The first sporadic groups were found by Mathieu in 1860s. The last sporadic group J4 was discovered in 1975 by Janko.
3
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(weak?) BN-Pair / Tits System for Sporadic Groups
Thanx to Humphreys and Koen for providing, that rank 1,2 is "geometrically unsatisfying" in the sense of Tits buildings and suggesting the notion of split BN-pairs as a tightning. But looking at the s …
- 1,846
20
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2
answers
1k
views
(weak?) BN-Pair / Tits System for Sporadic Groups
The structure of finite simple groups of Lie type of arbitrary rank can be described well via BN-pairs. BN-pairs basically generalize the Bruhat decomposition of matrices into monomial $N$ and triangu …
- 1,846
21
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Why are the sporadic simple groups HUGE?
Indeed the question is too vague for a precise answer, but nevertheless somehat natural ;-)
I want to give some more details and clearifications to the "hierarchy", that has been broached by Carnahan …
- 1,846