In Note M, Burnside (1955) states, "The contrast that these results shew between groups of odd and of even order suggests inevitably that simple groups of odd order do not exist." Of course, simple groups of prime order do exist, namely the groups for any prime . Therefore, Burnside conjectured that every finite simple group of non-prime order must have even order. The conjecture was proven true by Feit and Thompson (1963).

# Burnside's Conjecture

## See also

Abelian Group, Feit-Thompson Conjecture, Feit-Thompson Theorem, Simple Group
*This entry contributed by Nicolas
Bray*

## Explore with Wolfram|Alpha

## References

Burnside, W.*Theory of Groups of Finite Order, 2nd ed.*New York: Dover, 1955.Feit, W. and Thompson, J. G. "Solvability of Groups of Odd Order."

*Pacific J. Math.*

**13**, 775-1029, 1963.

## Referenced on Wolfram|Alpha

Burnside's Conjecture## Cite this as:

Bray, Nicolas. "Burnside's Conjecture." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/BurnsidesConjecture.html