Browsing by Author "Ligonnah, A."

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    Characterization of A8 by 3-Centralizers
    (University of Namibia, 2014) Ligonnah, A.
    Let G be a finite group containing a subgroup H isomorphic to an alternating group, An, such that G satisfies the 3-cycle property, namely ’for a 3-cycle x 2H, if xg 2H for any g 2 G, then g 2 H.’It is proved that for n = 8, G is isomorphic to LK, an extension of an elementary Abelian 2-group L by a group K isomorphic to either A8 or SL(5, 2). If G is simple, it is shown that G is isomorphic to A8 or SL(5, 2).
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    Characterization of An for n = 5, 6 by 3-centralizers
    (University of Namibia, 2014) Ligonnah, A.
    Let G be a finite group containing a subgroup H isomorphic to an alternating group, An, such that G satisfies the 3-cycle property, namely ’for a 3-cycle x 2 H, if xg 2 H for any g 2 G, then g 2 H.’ It is proved that G is isomorphic to LK, an extension of an Abelian 2-group L by a group K isomorphic to either A5 for n = 5; or A6 or A7 for n = 6. If G is simple, we establish that G is isomorphic to A5 for n = 5; or G is isomorphic to A6 or A7 for n = 6.