Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 937b84cd55ca…

magma 937b84cd55ca
Size
705
Isomorphism class hash
937b84cd55caa3b34022bcf7a7c3dab109101513651c454ebb31bd35a85652dc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:43:15
Display reorder
704,149,175,142,188,147,176,143,186,148,174,141,187,145,178,138,191,146,179,139,189,144,177,140,190,133,155,173,183,134,153,171,184,132,154,172,185,151,136,169,182,152,137,170,180,150,135,168,181,164,162,163,167,165,166,159,160,157,158,156,161,680,681,682,683,213,549,16,201,214,550,17,202,215,551,15,203,212,548,12,200,210,546,13,198,211,547,14,199,22,204,540,192,23,205,541,193,21,206,542,194,207,18,543,195,208,19,544,196,209,20,545,197,648,649,650,651,652,653,654,655,658,656,657,659,703,702,700,701,397,425,3,439,398,423,4,440,396,424,5,438,400,421,2,442,401,422,1,443,399,420,0,441,9,403,431,437,10,404,429,435,11,402,430,436,406,8,427,433,407,6,428,434,405,7,426,432,409,410,408,412,413,411,415,416,417,418,419,414,671,670,668,669,326,309,58,323,324,310,59,321,325,311,57,322,329,308,54,319,327,306,55,320,328,307,56,318,49,332,300,314,50,330,301,312,48,331,302,313,335,52,303,317,333,53,304,315,334,51,305,316,346,347,345,342,343,344,337,338,339,340,341,336,676,677,678,679,527,501,47,513,525,502,45,514,526,503,46,515,523,500,43,512,524,498,44,510,522,499,42,511,38,518,492,504,36,516,493,505,37,517,494,506,521,41,495,507,519,39,496,508,520,40,497,509,528,529,530,531,532,533,534,535,539,537,538,536,690,691,688,689,617,643,228,610,615,644,229,611,616,642,230,609,613,646,231,606,614,647,232,607,612,645,233,608,234,623,641,601,235,621,639,602,236,622,640,600,619,237,637,604,620,238,638,605,618,239,636,603,632,630,631,635,633,634,627,628,625,626,624,629,694,695,693,692,446,479,24,480,444,477,25,481,445,478,26,482,449,475,27,483,447,476,28,484,448,474,29,485,30,452,470,486,31,450,468,487,32,451,469,488,455,33,473,489,453,34,471,490,454,35,472,491,466,467,465,462,463,464,457,458,459,460,461,456,662,661,660,663,276,253,74,265,277,254,72,266,278,252,73,264,279,256,77,268,280,257,75,269,281,255,76,267,80,282,259,271,78,283,260,272,79,284,258,270,285,83,262,274,286,81,263,275,287,82,261,273,242,240,241,245,243,244,248,246,250,251,249,247,686,687,684,685,127,106,299,113,128,107,297,111,126,105,298,112,130,102,295,109,131,103,296,110,129,104,294,108,290,125,97,119,288,123,98,117,289,124,96,118,121,293,100,115,122,291,101,116,120,292,99,114,91,92,90,94,95,93,89,87,84,85,86,88,697,696,699,698,376,352,64,360,377,353,65,361,375,351,63,362,372,348,60,363,373,349,61,364,374,350,62,365,70,382,358,366,71,383,359,367,69,381,357,368,378,66,354,369,379,67,355,370,380,68,356,371,384,385,386,387,388,389,390,391,395,393,394,392,665,664,667,666,587,560,226,570,585,558,227,571,586,559,225,572,583,563,222,573,584,561,223,574,582,562,224,575,217,578,555,568,218,576,556,569,216,577,557,567,581,220,554,564,579,221,552,565,580,219,553,566,590,588,589,593,591,592,596,594,598,599,597,595,673,672,675,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#616ee92b4c2e3f87630606dae5e5d5a5d531c0e51b30b7b61db0c949f5d47644, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 17:43:16 · history