Maschke's Theorem states that if a finite group is represented on a vector space over a field whose characteristic does not divide the order of the group, then every representation of the group decomposes as a direct sum of irreducible representations. Named for Heinrich Maschke, it guarantees that representation theory over such fields reduces to the study of irreducible pieces.
Facts
StatementMaschke's theorem states that if the order of a finite group G is not divisible by the characteristic of a field K, then every finite-dimensional representation of G over K is completely reducible, decomposing as a direct sum of irreducible representations. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Maschke's Theorem (Wikipedia)
Wikimedia FoundationLead paragraph, first sentenceQuote, Lead paragraph, first sentence
In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces.
2. Heinrich Maschke, Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsCareer paragraph, Maschke's theorem sentenceQuote, Career paragraph, Maschke's theorem sentence
He is best known today for Maschke's theorem, which he published in 1899, which states that if the order of the finite group
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.