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- W68663128 abstract "In [Akbari and Moghaddamfar, Recognizing by order and degree pattern of some projective special linear groups, {it Internat. J. Algebra Comput.}, 2012] the authors possed the following problem: {bf Problem.} {it Is there a simple group which is $k$-fold OD-characterizable for $kgeq3 ?$ } In this paper as the main result we give positive answer to the above problem and we introduce two simple groups which are $k$-fold OD-characterizable such that $kgeq6$. Also in [R. Kogani-Moghadam and A. R. Moghaddamfar, Groups with the same order and degree pattern, {it Science China Mathematics}, 2012], the authors possed two conjectures as follows: {bf Conjecture 1.} {it All alternating groups $A_m$ with $m not= 10$ are OD-characterizable.} {bf Conjecture 2.} {it All symmetric groups $S_m$, with $m not= 10$, are $n$-fold OD-characterizable, where $nin{1, 3}$.} In this paper we find some alternating and some symmetric groups such that these conjectures are not true for them." @default.
- W68663128 created "2016-06-24" @default.
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- W68663128 date "2014-09-28" @default.
- W68663128 modified "2023-09-27" @default.
- W68663128 title "The Answers to a Problem and Two Conjectures about OD-Characterization of Finite Groups" @default.
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