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the number of maximal subgroups and probabilistic generation of finite groups
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نویسنده
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ballester-bolinches adolfo ,esteban-romero ramón ,jiménez-seral paz ,meng hangyang
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منبع
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international journal of group theory - 2020 - دوره : 9 - شماره : 1 - صفحه:31 -42
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چکیده
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In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. as a consequence, new bounds for the number of random generators needed to generate a finite d-generated group with high probability which are significantly tighter than the ones obtained in the paper of jaikin-zapirain and pyber (random generation of finite and profinite groups and group enumeration, ann. math., 183 (2011) 769–814) are obtained. the results of jaikin-zapirain and pyber, as well as other results of lubotzky, detomi, and lucchini, appear as particular cases of our theorems.
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کلیدواژه
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finite group ,maximal subgroup ,probabilistic generation ,primitive group
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آدرس
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universitat de valencia, departament de matematiques, spain, universitat de valencia, departament de matematiques, spain. universitat politecnica de valencia, institut universitari de matematica pura i aplicada, spain, universidad de zaragoza, departamento de matematicas, spain, universitat de valencia, departament de matematiques, spain
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پست الکترونیکی
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menghangyanges@gmail.com, hangyangmenges@gmail.com
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Authors
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