Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

That is -- is it true that if projective $k[G]$-modules have same composition factors then they are isomorphic?

This is easy to see for $\text{char}(k)=0$, or if $G$ is a composition of a $p$-group and a $p'$-group. Serre in "Linear Representations of Finite Groups" (a remark in 16.2 after Corr.2) states this as a well-known fact: "Indeed we know that the equality $[P] = [ P']$ (...) is equivalent to $P = P'$)". But unfortunately no references.

share|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.