Restricted Burnside group:RB(2,5)

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Definition

This group is defined as the restricted Burnside group with parameters 2,5. In other words, it is the quotient by the finite residual of the Burnside group $B(2,5)$, which in turn is defined as the quotient of the free group of rank two by the intersection of all its normal subgroups of finite index.

The group turns out to be a finite group (this is a special case of Kostrikin's theorem on restricted Burnside problem). Thus, it can also be defined as the largest size finite group that is a 2-generator group and has exponent five.

Arithmetic functions

Function	Value	Similar functions	Explanation
underlying prime of p-group	5
prime-base logarithm of order	34	groups with same prime-base logarithm of order
max-length of a group	34		max-length of a group equals prime-base logarithm of order for group of prime power order
chief length	34		chief length equals prime-base logarithm of order for group of prime power order
composition length	34		composition length equals prime-base logarithm of order for group of prime power order
nilpotency class	12