Left Semidirect Product ⋋

Semantic identity and intent

Characters to distinguish

• + — Plus Sign
• − — Minus Sign
• × — Multiplication Sign

Use ⋋ in the right format

Meaning and usage

Represents the left semidirect product, a specialized mathematical operator or relation whose exact definition depends on context.

Define the operands and result type when first using ⋋; specialized operator symbols should not be treated as ordinary multiplication or punctuation.

Pronunciation: left semidirect product

Formula examples

How to type Left Semidirect Product

Windows

Use Character Map or enter U+22CB in a Unicode-aware application.

macOS

Open Character Viewer with Control–Command–Space and search by the symbol name.

Microsoft Word

In an equation, type \leftthreetimes and press Space when Word supports the command.

iPhone and iPad

Copy and paste ⋋, or use a math/LaTeX app. The standard iOS keyboard may not expose every mathematical symbol.

Android

Copy and paste ⋋, or use a math keyboard or LaTeX editor. Keyboard layouts vary by device and app.

Google Docs

For plain text, paste ⋋ or use Insert → Special characters. For structured math, use the equation editor and verify \leftthreetimes.

Excel

Paste ⋋ into a cell or use Insert → Symbol when available. Ordinary cells preserve the character but do not interpret LaTeX commands.

Common mistakes

• Preserve grouping, operator order, and spacing around ⋋; Define the operands and result type when first using ⋋; specialized operator symbols should not be treated as ordinary multiplication or punctuation.
• For plain text, copy ⋋ as U+22CB; for structured equations, use \leftthreetimes in math mode. A look-alike glyph or image can break search, accessibility, or parsing when the intended character is Left Semidirect Product.

When to use ⋋

• Use ⋋ in plain text when a Unicode character is appropriate and the destination preserves U+22CB.
• Use \leftthreetimes in an equation editor when mathematical spacing or structure matters.
• Define the local meaning when Left Semidirect Product is used in algebra, graph theory with a field-specific convention.

Look-alikes and related characters

• + — Plus Sign
• − — Minus Sign
• × — Multiplication Sign

Font and compatibility notes

Glyph shape can vary by font. Verify the code point after copying, and prefer LaTeX or MathML for structured equations.

Review and source notes

Quality tier: core

Last reviewed: 2026-07-26

Review method: Checked Left Semidirect Product against its Unicode identity, LaTeX representation, HTML serialization, MathML token, and copy-and-paste behavior.

Verified against: Unicode Standard, Unicode mathematical notation guidance, and established LaTeX/MathML syntax.

Reference sources

• The Unicode StandardUnicode Consortium — Character identity, encoding, names, and conformance.
• Unicode Character Code ChartsUnicode Consortium — Code points and official character charts.
• Unicode Technical Report #25: Unicode Support for MathematicsUnicode Consortium — Mathematical character usage, variants, and notation support.
• LaTeX Project DocumentationThe LaTeX Project — LaTeX syntax, authoring model, and official documentation links.
• MathML CoreW3C — Semantic web mathematics elements and browser behavior.

Frequently asked questions