Equation 677 Database

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Magma caaa25226804…

magma caaa25226804
Size
705
Isomorphism class hash
caaa25226804058f2efbddba6563d7e7a901349b35e9c797ed6cb9cfb78510ad
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 15:13:31
Display reorder
660,574,4,567,577,578,594,5,587,597,598,554,3,547,557,558,634,1,627,637,638,0,654,647,657,658,2,614,607,617,618,534,10,527,537,538,494,11,487,497,498,514,9,507,517,518,6,445,442,447,448,7,473,467,475,476,8,433,427,435,436,696,699,690,685,570,18,563,576,579,590,19,583,596,599,550,20,543,556,559,630,21,623,636,639,22,650,643,656,659,23,610,603,616,619,530,16,522,536,539,490,17,482,496,499,510,15,502,516,519,12,456,452,446,449,13,469,462,474,477,14,429,423,434,437,693,702,692,687,114,92,284,219,229,115,90,282,220,230,116,91,283,221,228,117,95,287,218,232,93,118,285,216,233,94,119,286,217,231,112,87,279,225,235,113,88,280,226,236,111,89,281,227,234,86,108,278,224,238,84,109,276,222,239,85,110,277,223,237,661,662,668,666,403,166,319,190,195,404,167,320,191,196,402,165,318,189,197,406,162,322,186,194,163,407,323,187,192,164,405,321,188,193,401,157,317,181,201,399,158,315,182,202,400,156,316,180,203,160,397,313,184,200,161,398,314,185,198,159,396,312,183,199,669,678,681,664,565,97,562,566,564,585,98,582,586,584,545,96,542,546,544,625,100,622,626,624,101,645,642,646,644,99,605,602,606,604,524,103,525,526,523,484,104,485,486,483,504,102,505,506,503,106,440,441,454,453,107,464,465,466,463,105,425,421,426,424,695,704,700,697,560,39,561,569,572,580,40,581,589,592,541,41,540,549,552,621,38,620,629,632,36,641,640,649,652,37,600,601,609,612,521,45,520,529,532,481,46,480,489,492,501,47,500,509,512,44,451,450,455,457,42,461,460,468,471,43,422,420,428,431,698,701,703,694,575,26,568,571,573,595,24,588,591,593,555,25,548,551,553,635,29,628,631,633,27,655,648,651,653,28,615,608,611,613,535,32,528,531,533,495,30,488,491,493,515,31,508,511,513,35,458,459,443,444,33,479,478,470,472,34,438,439,430,432,691,689,686,688,307,48,291,379,355,308,49,292,380,356,306,50,293,378,354,310,51,290,382,358,52,311,288,383,359,53,309,289,381,357,305,54,297,377,353,303,55,298,375,351,304,56,299,376,352,57,301,296,373,349,58,302,294,374,350,59,300,295,372,348,676,672,663,679,174,266,152,343,130,175,264,150,344,131,176,265,151,342,129,177,269,155,346,126,267,178,153,347,127,268,179,154,345,128,172,272,147,341,121,173,270,148,339,122,171,271,149,340,120,275,168,146,337,124,273,169,144,338,125,274,170,145,336,123,667,684,670,675,415,246,75,212,391,416,247,76,210,392,414,248,77,211,390,418,249,74,215,394,250,419,72,213,395,251,417,73,214,393,413,244,81,207,389,411,245,82,208,387,412,243,83,209,388,240,409,80,206,385,241,410,78,204,386,242,408,79,205,384,683,680,682,671,253,142,71,367,331,254,143,69,368,332,252,141,70,366,330,256,138,67,370,334,139,257,68,371,335,140,255,66,369,333,259,133,62,365,329,260,134,60,363,327,258,132,61,364,328,136,262,65,361,325,137,263,63,362,326,135,261,64,360,324,674,665,677,673 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#0c204955552ad126415d2d3170da1bc3e83549814dfd47378340ca39d32aede4, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:13:33 · history