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Prime review pp. Journal of Business Finance and Accounting, 9, The Decline and Resurgence of Congress. If N is a pi -group for some prime graph component of G and m1 ; m2 ;. Therefore, a follows. Then we obtain a contradiction. We consider the following two cases: Case 1. An easy investigation shows that this is a contradiction.
Case 2. An easy calculation shows that such equalities are impossible.
Then G is neither a Frobenius group nor a 2-Frobenius group. G is not a Frobenious group otherwise by lemma 2. Therefore G is not a Frobenious group. Let G be a 2-Frobenius group and q is even.
By Lemma 2. Let G be a finite group. The first part of the lemma follows from the above lemmas since the prime graph of M has two prime graph components. Proof of the Main Theorem By Lemma 2. We summarize the relevant information in Tables 1—3 below: We now proceed the proof in the following steps: Step 1.
Characterization by Prime Graph of PGL(2, PK) Where P and k > 1 are odd
By lemma 2. Step 2. Step 3. Step 4. Step 5. Here we get a contradiction similarly. Step 6. We proceed similarly. Step 7. Since r b 5 we have q 15 j jGj, which is a contradiction by Lemma 2.
Gorenstein : Classifying the finite simple groups
Then we proceed similarly. Step 8. This is similar to cases 8. Step 9.
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Step Again by the table of sporadic simple group 37 is an odd order component of Ly and J4. The proof of the main theorem is now completed. It is a well known conjecture of J. We can give a positive answer to this conjecture by our characterization of the groups under discussion. Corollary 3. By [2, Lemma 1. So the main theorem implies this corollary. Wujie Shi and Bi Jianxing in  put forward the following conjec- ture: Conjecture.
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Alavi This conjecture is valid for sporadic simple groups , groups of alternating type , and some simple groups of Lie types [14, 15, 16]. As a consequence of the main theorem, we prove the validity of this conjecture for the groups under discussion. References 1. Chen, G. Southwest China Normal Univ.