OD-Characterization of alternating and symmetric groups of degrees 16 and 22

Moghaddamfar, A. R.; Zokayi, A. R.

doi:10.1007/s11464-009-0037-1

Cited by 25 publications

(18 citation statements)

References 12 publications

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“…So far there is no alternating group not OD-characterizable is found. Hence, the authors in [5] put forward the following conjecture:…”

Section: Od-characterizable Of the Alternating Groupsmentioning

confidence: 99%

“…On the other hand , by Lemma 2.4. we observe that 103 E 1T(G) <;;; 1T(Aut(S)). Thus, we may assume that 103 divides the order of Out (5).…”

Section: Od-characterizable Of the Alternating Groupsmentioning

confidence: 99%

“…Given a finite group G. denote by Soe( G) the socle of G which is the subgroup generated by the set of all minimal normal In a series of articles (Ref. to [1,3,4,5,6,7,8]), it was shown that many finite almost simple groups arc OD-characterizable, which are included in the following proposition.…”

Section: Introductionmentioning

confidence: 99%

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OD-Characterization of Alternating and Symmetric Groups of Degree 106 and 112

Yan¹,

Chen²

2011

Proceedings of the International Conference on Algebra 2010

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The degree pattern of a finite group G associated to its prime graph has been introduced in [IJ and it is proved that the following simple groups are uniquely determined by their degree patterns and orders: all sporadic simple groups , alternating groups .4.p (p 2: 5 is a twin prime) and some simple groups of Lie type. In the present paper. we continue this investigation. In particular, we show that the alternating groups .4.106 and A1l2 are OD-characterizable. We will also show that the symmetric groups 5 106 and 5112 are 3-fold OD-characterizable.

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“…So far there is no alternating group not OD-characterizable is found. Hence, the authors in [5] put forward the following conjecture:…”

Section: Od-characterizable Of the Alternating Groupsmentioning

confidence: 99%

“…On the other hand , by Lemma 2.4. we observe that 103 E 1T(G) <;;; 1T(Aut(S)). Thus, we may assume that 103 divides the order of Out (5).…”

Section: Od-characterizable Of the Alternating Groupsmentioning

confidence: 99%

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OD-Characterization of Alternating and Symmetric Groups of Degree 106 and 112

Yan¹,

Chen²

2011

Proceedings of the International Conference on Algebra 2010

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“…A 26 2 22 · 3 10 · 5 6 · 7 3 · 11 2 · 13 2 · 17 · 19 · 23 (7,8,7,7,5,5,4,4,1) S 26 2 23 · 3 10 · 5 6 · 7 3 · 11 2 · 13 2 · 17 · 19 · 23 (8,8,7,7,5,5,4,4, 2) A 34 2 31 · 3 15 · 5 7 · 7 4 · 11 3 · 13 2 · 17 2 · 19 · 23 · 29 · 31 (9, 10, 9, 8, 8, 7, 6, 6, 5, 3, 1) S 34 2 32 · 3 15 · 5 7 · 7 4 · 11 3 · 13 2 · 17 2 · 19 · 23 · 29 · 31 (10, 10,9,8,8,7,6,6,5,3, 2) A 40 2 37 · 3 18 · 5 9 · 7 5 · 11 3 · 13 3 · 17 2 · 19 2 · 23 (10,11,10,10,9,8,8,7,7, · 29 · 31 · 37 5, 4, 1) S 40 2 38 · 3 18 · 5 9 · 7 5 · 11 3 · 13 3 · 17 2 · 19 2 · 23 (11,11,10,10,9,8,8,7,7, · 29 · 31 · 37 5, 4, 2) A 46 2 41 · 3 21 · 5 10 · 7 6 · 11 4 · 13 3 · 17 2 · 19 2 · 23 2 (12, 13, 12, 11, 10, 10, 9, 8, · 29 · 31 · 37 · 41 · 43 8, 7, 6, 4, 3, 1) S 46 2 42 · 3 21 · 5 10 · 7 6 · 11 4 · 13 3 · 17 2 · 19 2 · 23 2 (13, 13, 12, 11, 10, 10, 9, Table 2 Connected compon...…”

Section: Lemma 1 Let M = P α1unclassified

Recognizing alternating groups A p+3 for certain primes p by their orders and degree patterns

Hoseini

Moghaddamfar

2010

Front. Math. China

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The degree pattern of a finite group M has been introduced by A. R. Moghaddamfar et al. [Algebra Colloquium, 2005, 12(3): 431-442]. A group M is called k-fold OD-characterizable if there exist exactly k nonisomorphic finite groups having the same order and degree pattern as M. In particular, a 1-fold OD-characterizable group is simply called OD-characterizable. In this article, we will show that the alternating groups A p+3 for p = 23, 31, 37, 43 and 47 are OD-characterizable. Moreover, we show that the automorphism groups of these groups are 3-fold OD-characterizable. It is worth mentioning that the prime graphs associated with all these groups are connected.

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“…(3) A n with that either 5 Ä n Ä 100 and n ¤ 10 or n D 106; 112, is OD-characterizable [5,7,[9][10][11][12]. (4) A pC5 with p Ä 1000 a prime is OD-characterizable [13].…”

Section: Introductionmentioning

confidence: 99%