Equation 677 Database

← all  ·  ← by size  ·  ← size 369

Magma 43260b92af80…

magma 43260b92af80
Size
369
Isomorphism class hash
43260b92af802955f5a1b0127e1a5caabebd3ad3d19c1f7de614caf02378f525
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 368) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 16:02:49
Display reorder
360,361,362,363,364,365,366,367,368,10,9,17,14,15,16,12,13,11,54,55,56,60,61,62,57,58,59,100,99,101,105,106,107,102,103,104,144,145,146,150,151,152,147,148,149,190,189,191,195,196,197,192,193,194,234,235,236,240,241,242,237,238,239,281,280,279,286,287,285,282,283,284,326,325,324,330,331,332,327,328,329,31,30,32,28,27,29,33,34,35,77,75,76,73,72,74,80,78,79,120,122,121,118,117,119,123,124,125,167,165,166,163,162,164,168,169,170,212,210,211,207,208,209,213,214,215,257,255,256,253,252,254,258,259,260,302,300,301,298,299,297,303,304,305,347,345,346,343,342,344,348,349,350,42,44,43,41,39,40,38,37,36,88,89,87,86,84,85,81,83,82,132,134,133,131,129,130,126,128,127,179,177,178,176,174,175,171,173,172,224,222,223,221,219,220,217,218,216,269,267,268,266,264,265,261,263,262,314,312,313,311,309,310,308,306,307,359,357,358,355,356,354,353,352,351,26,25,24,18,20,19,22,23,21,70,71,69,65,63,64,66,67,68,116,115,114,110,109,108,111,112,113,160,161,159,155,153,154,156,157,158,205,206,204,200,198,199,201,202,203,250,251,249,245,243,244,246,247,248,295,296,294,290,288,289,291,292,293,340,341,339,334,335,333,337,338,336,0,1,2,3,4,5,6,7,8,45,46,47,48,49,50,51,52,53,90,91,92,93,94,95,96,97,98,135,136,137,138,139,140,141,142,143,180,181,182,183,184,185,186,187,188,225,226,227,228,229,230,231,232,233,270,271,272,273,274,275,276,277,278,315,316,317,318,319,320,321,322,323 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 369 = 9 + 5*72, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#0dd86070b42eb55a1a255aa4e6a7ee17e6a356f4c97ab7c8fc1c48e3adb556bb, M = {72, 73, 74, 75, 76, 77, 78, 79, 80} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 72): MacNeish's product over GF(8) x GF(9); GF(8) = F_2[x]/(x^3 + x + 1), GF(9) = F_3[x]/(x^2 + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 1.

last edited by qawbecrdtey at 2026-10-07 16:02:51 · history