Baby monsters group

In group theory , the baby monster group (abbreviation: B) is a group of order

   2 ⁴¹ · 3 ¹³ · 5 ⁶ · 7 ² · 11 · 13 · 17 · 19 · 23 · 31 · 47

= 4154781481226426191177580544000000

≈ 4 · 10 ³³ .

It is a finite simple group . It is one of the sporadic groups , and after the monster group the one with the second highest order. Its discoverer was Bernd Fischer . Then it was first designed by Charles Sims .

The smallest matrix representation of the baby monster group has the size 4370 over the finite body of order 2. In the meantime, permutation representations of this group can also be calculated.

literature

• Robert A. Wilson: Conjugacy Class Representatives in Fischer's Baby Monster . In: LMS Journal of Computation and Mathematics . tape 5 , 2002, p. 175–180 (English, online [PDF; 163 kB ]).
• Jürgen Müller: On the action of the sporadic simple Baby Monster group on its conjugacy class 2B (PDF file; 224 kB)
• Robert A. Wilson: More on maximal subgroups of the Baby Monster, 1993

Individual evidence

1. ^ Mark Ronan, Symmetry and the Monster: One of the Greatest Quests of Mathematics . Oxford University Press, 2006, ISBN 0-19-280722-6 , pp. 246 ( limited preview in Google Book search).
2. ^ L. Corwin, IM Gelfand, James Lepowsky: The Gelfand Mathematical Seminars, 1990-1992, 1993, p. 141
3. ↑ Eric Robinson, Gene Cooperman: A parallel architecture for disk-based computing over the Baby Monster and other large finite simple groups, 2006

Web links

• Eric W. Weisstein: Baby Monster Group. In: Wolfram MathWorld. Retrieved January 21, 2018 .