The Maximal Tori in The Finite Chevalley Groups of Type E6E7And E8

Deriziotis, D. I.; Fakiolas, A.P.

doi:10.1080/00927879108824176

Cited by 46 publications

(42 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…P r o o f o f t h e C l a i m. One has G ∼ = PSL (3,4), and it has order 2 6 × 3 2 × 5 × 7. According to Table 2 cyclic groups can have order dividing either of 3 2 , 7 and 2 6 .…”

Section: Vol 85 2005mentioning

confidence: 99%

Maximal cyclic subgroups and prime divisors in finite groups

Arad

Herfort

2005

Arch. Math.

View full text Add to dashboard Cite

H e r r n P r o f e s s o r O t t o H. K e g e l z u m 7 0. G e b u r t s t a g g e w i d m e t Abstract. Let G be a finite group with no chief factor simple of Lie type E 8 (q) and C a cyclic subgroup of largest order in G. It is shown that at most two primes in the open interval ([|C|/2], |C|) divide |G|. 0. Introduction. N o t a t i o n 1. For a finite group G and a cyclic subgroup C of largest possible order in G define T := {p ∈ π(G) | [ |C| 2 ] < p < |C|}. The main goal of this paper is to prove the following Theorem: Main Theorem. Let G be a finite group with no chief factor of Lie type E 8 (q) and C a cyclic subgroup of largest order in G. Then 0 |T | 2.

show abstract

“…P r o o f o f t h e C l a i m. One has G ∼ = PSL (3,4), and it has order 2 6 × 3 2 × 5 × 7. According to Table 2 cyclic groups can have order dividing either of 3 2 , 7 and 2 6 .…”

Section: Vol 85 2005mentioning

confidence: 99%

Maximal cyclic subgroups and prime divisors in finite groups

Arad

Herfort

2005

Arch. Math.

View full text Add to dashboard Cite

show abstract

“…In the notation of the proof of Theorem 5.4.1 (and using the crudest bounds), we determine that n 0 = 27, and for each n < n 0 , we obtain the following values q 0 : Verifying which of these finitely many pairs satisfy the necessary divisibility relations, we see that the only possible pairs (n, q) lie in the following set: (2,4), (2,5), (2,7), (2,9), (3,2), (3,3), (4, 2), (4, 3)}.…”

Section: The Symplectic and Odd-dimensional Orthogonal Groupsmentioning

confidence: 99%

“…PSL n (q) with q can occur as a composition factor of an -Brauer rational group if and only if (n, q) ∈ {(2, 4), (2,5), (2, 7), (2,8), (2,9), (2,25), (3,2), (3,4), (4, 2), (4, 3)}.…”

Section: The Linear Groupsmentioning

confidence: 99%

“…As a Zsigmondy prime does not exist for 2 6 − 1, we first note that O + 8 (2) is rational. Now, we must determine which pairs (n, q) satisfy the divisibility relations Verifying which of the (finitely many) remaining pairs (n, q) satisfy the necessary divisibility relation, we see that S can occur as a composition factor of an quadratic rational group only if (n, q) ∈ {(4, 2), (4,3), (4,4), (4,5), (4,9), (6, 2)}.…”

Section: The Even-dimensional Orthogonal Groupsmentioning

confidence: 99%

“…Then, for each 3 ≤ n ≤ 22, we may choose q 0 as follows: Verifying which of these (finitely many) pairs (n, q) satisfy φ(N ) n | 2| Out(S)| (see the Appendix for the complete set of computations), we determine that S = PSL n (q) can occur as a composition factor of a quadratic rational group only if (n, q) ∈ {(2, 4), (2,5), (2, 7), (2,8), (2,9), (2,11), (2,16), (2,19), (2,23), (2,27), (2,31), (3,2), (3,3), (3,4), (3,7), (3,16) is to occur as a composition factor of a quadratic rational group, it must be the case…”

Section: Lemma 425 Let S Be a Generator Of The Unique Subgroup Of mentioning

confidence: 99%

See 2 more Smart Citations