*Vladimir Ignatowski* (1875-1942) was a Russian physicist. “In 1910 he was to first who tried to derive the Lorentz transformation by group theory only using the relativity principle (postulate), and without the postulate of the constancy of the speed of light.” K M Browne gave a simplified derivation in the *European Journal of Physics*, 39 (2018) 025601, from which the key steps are presented below, followed by the corresponding steps for a dual transformation, switching space and time.

This is a derivation of the Ignatowsky transformation in which the axes *x*, *y*, and *z* are taken to represent *space* axes *r*_{x}, *r*_{y}, and *r*_{z} with *time* *t*. The relativity postulate is taken to be: *a valid relativistic transformation must be identical in all inertial frames*.

**Step 1**. To find a valid transformation, we take the usual inertial reference frames *S* and *S*′ (the latter moving at velocity *v* in the +*x* direction relative to the former) for which intra-frame space is Euclidean but inter-frame space (measured from one frame to the other) may be non-Euclidean. Linear equations are necessary so that an event in one frame appears as a single event, without echoes, in the other. Initial conditions are *x*′ = *x* = 0 when time *t*′ = *t* = 0. We expect the generalised *x* equation to be the Euclidean equation *x*′ = *x* − *vt* with an added multiplier, and if time is the fourth dimension, then the time equation will be similar but with two additional multipliers. The second of these, *n*, having the dimension of inverse velocity squared, is required to make the equation dimensionally correct. The *y* and *z* coordinates are not expected to be affected by *x* and *t*. The generalised transformation and its inverse are then