Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma bbadddeab7ea…

magma bbadddeab7ea
Size
595
Isomorphism class hash
bbadddeab7ea84bdb48dc46a3a990781cc76b5712d3aa8718f617ab8b0fde871
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 11:35:49
Display reorder
33,32,28,29,30,31,43,48,44,45,46,47,112,111,113,114,115,110,415,414,416,419,417,418,457,456,458,461,459,460,533,525,552,568,570,277,276,174,274,275,219,191,120,121,117,118,119,142,141,143,144,139,140,1,4,2,223,224,3,228,227,180,181,49,50,99,98,100,96,97,233,207,258,206,259,208,209,231,184,232,185,230,183,186,82,83,79,80,81,502,501,503,499,500,498,365,364,363,360,361,362,468,470,469,472,473,471,427,426,428,430,431,429,405,407,406,404,402,403,486,488,487,490,491,489,485,484,483,481,482,480,517,545,535,536,511,512,510,572,561,564,560,588,559,593,562,575,130,129,132,133,128,131,72,71,67,68,69,70,53,52,54,55,56,51,13,12,14,15,16,11,37,36,38,39,34,35,21,20,17,18,19,225,249,158,250,248,199,200,268,267,168,265,266,216,192,134,135,136,137,138,339,341,340,336,337,338,408,410,409,412,413,411,453,455,454,451,452,450,304,303,305,301,302,300,507,509,508,506,504,505,448,447,449,446,444,445,295,294,296,297,298,299,531,529,513,526,527,524,546,566,548,549,551,583,591,574,587,555,108,107,104,105,106,109,89,88,84,85,86,87,126,125,127,122,123,124,78,77,73,74,75,76,59,58,60,61,62,57,149,148,146,147,145,280,286,175,287,283,278,279,282,284,159,285,281,253,242,156,152,153,154,155,479,478,477,476,474,475,289,290,288,292,293,291,332,331,330,333,334,335,316,315,317,313,314,312,371,370,369,367,368,366,352,351,353,350,348,349,395,394,393,391,392,390,537,538,516,522,514,523,515,578,558,576,556,594,584,569,579,573,5,10,7,8,9,6,0,222,176,220,177,221,203,202,251,204,252,201,226,178,179,42,40,41,171,170,169,173,272,269,172,273,270,217,218,271,214,263,215,264,212,213,245,198,246,196,247,197,205,257,254,160,255,256,375,377,376,372,373,374,318,320,319,322,323,321,465,467,466,463,464,462,492,494,493,495,496,497,329,328,327,325,326,324,443,442,441,438,439,440,309,311,310,308,306,307,540,544,532,528,530,534,519,565,554,553,592,590,581,547,585,582,27,26,23,24,25,22,150,241,238,151,239,240,190,189,235,236,116,237,234,187,188,103,101,102,63,66,64,65,182,229,244,243,193,194,195,157,166,165,161,162,163,164,90,95,91,92,93,94,167,211,260,261,262,210,356,355,354,359,357,358,420,422,421,424,425,423,347,346,345,342,343,344,436,435,437,433,434,432,386,385,384,388,389,387,382,381,383,380,378,379,397,396,398,399,400,401,521,520,541,542,518,539,543,577,567,580,557,586,563,550,589,571 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = the submagma generated by {36, 48} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 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: 85.

last edited by qawbecrdtey at 2026-10-06 11:35:50 · history