Equation 677 Database

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Magma 759330768311…

magma 759330768311
Size
705
Isomorphism class hash
7593307683111d7446585edb0989c7488c5ae3a819f12c87c7c88cb6cfe01242
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 19:16:54
Display reorder
660,567,588,580,100,555,101,568,589,581,556,99,569,590,579,557,96,566,591,576,554,97,564,592,577,552,98,565,593,578,553,573,594,586,106,561,574,595,587,107,562,575,596,585,105,563,572,597,582,102,560,570,598,583,103,558,571,599,584,104,559,687,688,686,685,287,255,246,338,269,336,285,256,247,267,337,286,257,248,268,341,283,254,249,265,339,284,252,250,266,340,282,253,251,264,278,261,244,344,275,276,262,245,342,273,277,263,243,343,274,281,260,240,347,271,279,258,241,345,272,280,259,242,346,270,703,704,701,702,537,507,551,138,521,139,538,508,549,519,140,539,509,550,520,141,536,506,547,517,142,534,504,548,518,143,535,505,546,516,528,513,542,136,527,529,514,540,137,525,530,515,541,135,526,531,512,545,132,523,532,510,543,133,524,533,511,544,134,522,671,672,670,669,195,225,209,351,239,352,196,226,207,237,353,197,227,208,238,350,194,224,205,235,348,192,222,206,236,349,193,223,204,234,201,216,215,357,230,202,217,213,358,228,203,218,214,359,229,200,219,211,356,233,198,220,212,354,231,199,221,210,355,232,679,680,678,677,388,370,398,92,372,90,389,371,396,373,91,387,369,397,374,95,384,366,401,375,93,385,367,399,376,94,386,368,400,377,394,361,404,87,378,395,362,402,88,379,393,360,403,89,380,390,364,407,86,381,391,365,405,84,382,392,363,406,85,383,692,691,690,689,464,177,161,65,54,63,462,178,159,55,64,463,179,160,56,61,467,176,157,57,62,465,174,158,58,60,466,175,156,59,459,168,167,71,52,460,169,165,69,53,461,170,166,70,51,458,171,163,67,48,456,172,164,68,49,457,173,162,66,50,699,700,698,697,24,116,11,22,79,23,25,114,9,80,21,26,115,10,78,18,27,119,7,82,19,28,117,8,83,20,29,118,6,81,30,111,2,13,77,31,112,1,14,75,32,113,0,12,76,33,110,5,16,73,34,108,3,17,74,35,109,4,15,72,663,664,662,661,612,638,628,42,604,43,613,636,629,605,44,614,637,627,603,45,615,641,624,600,46,616,639,625,601,47,617,640,626,602,618,644,634,40,610,619,642,635,41,611,620,643,633,39,609,621,647,630,36,606,622,645,631,37,607,623,646,632,38,608,682,683,684,681,495,478,476,183,487,184,496,479,474,488,185,497,477,475,486,182,659,656,657,658,180,650,649,648,651,181,655,653,652,654,498,484,471,189,491,499,485,472,190,489,500,483,473,191,490,501,480,470,188,494,502,481,468,186,492,503,482,469,187,493,695,696,693,694,422,449,432,131,410,129,420,447,433,408,130,421,448,434,409,127,425,445,435,413,128,423,446,436,411,126,424,444,437,412,428,455,438,122,416,426,453,439,120,414,427,454,440,121,415,431,451,441,125,419,429,452,442,123,417,430,450,443,124,418,667,668,665,666,333,309,297,144,323,145,334,310,298,321,146,335,311,299,322,147,332,308,296,319,148,330,306,294,320,149,331,307,295,318,324,300,288,150,314,325,301,289,151,312,326,302,290,152,313,327,303,291,153,317,328,304,292,154,315,329,305,293,155,316,675,676,673,674 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#9741437d1171904ffa64043ea6d962aefa7dc37d5417f733d15a56c498f18cdb, 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 19:16:55 · history