Equation 677 Database

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Magma c71450e60955…

magma c71450e60955
Size
705
Isomorphism class hash
c71450e6095556dc25af2d28a55dc033ab10600cc3859c59f19e6b8653daf8c9
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 21:10:37
Display reorder
704,91,69,99,74,92,100,72,70,90,71,101,73,98,94,68,77,96,95,66,75,97,93,67,76,105,89,80,60,106,87,78,61,107,88,79,62,85,104,83,63,86,102,81,64,84,103,82,65,114,115,116,117,118,119,112,113,110,108,109,111,683,681,682,680,279,25,298,265,280,299,266,26,281,24,297,264,294,278,28,268,295,276,29,269,296,277,27,267,289,285,271,31,290,286,272,32,288,287,270,30,284,292,274,34,282,293,275,35,283,291,273,33,648,649,650,651,652,653,654,655,658,656,657,659,701,702,700,703,182,598,198,177,180,199,178,599,181,597,200,179,201,185,594,176,202,183,595,174,203,184,596,175,196,188,168,589,197,186,169,590,195,187,170,588,191,192,171,592,189,193,172,593,190,194,173,591,208,209,207,204,205,206,214,215,212,210,211,213,669,670,668,671,531,145,497,517,532,495,518,146,533,144,496,516,493,530,148,520,494,528,149,521,492,529,147,519,503,537,523,151,501,538,524,152,502,539,522,150,536,499,526,154,534,500,527,155,535,498,525,153,506,504,505,509,507,508,512,510,514,515,513,511,679,677,678,676,243,137,262,235,244,263,236,135,245,136,261,234,258,242,133,238,259,240,134,239,260,241,132,237,253,249,233,143,254,250,231,141,252,251,232,142,248,256,229,139,246,257,230,140,247,255,228,138,226,227,225,222,223,224,217,218,219,220,221,216,689,691,688,690,374,55,391,369,372,392,370,56,373,54,390,371,394,377,58,368,395,375,59,366,393,376,57,367,389,380,360,53,387,378,361,51,388,379,362,52,383,385,363,49,381,386,364,50,382,384,365,48,349,350,348,352,353,351,355,356,357,358,359,354,692,695,693,694,628,123,638,613,629,636,614,124,627,125,637,612,641,624,122,616,639,625,120,617,640,626,121,615,644,634,619,129,642,635,620,130,643,633,618,131,630,647,622,128,631,645,623,126,632,646,621,127,602,600,601,605,603,604,608,606,610,611,609,607,662,661,660,663,417,15,422,399,418,420,400,16,419,17,421,401,425,416,14,398,423,414,12,396,424,415,13,397,428,408,405,21,426,409,406,22,427,410,407,23,411,431,404,20,412,429,402,18,413,430,403,19,443,441,442,439,440,438,434,432,436,437,435,433,685,687,684,686,473,5,485,461,471,483,459,3,472,4,484,460,481,469,0,457,482,470,2,458,480,468,1,456,491,479,467,11,489,477,465,9,490,478,466,10,475,487,463,7,476,488,464,8,474,486,462,6,444,445,446,447,448,449,450,451,455,453,454,452,698,696,699,697,548,159,558,586,546,559,587,160,547,161,560,585,561,551,158,582,562,549,156,583,563,550,157,584,556,543,577,165,557,544,578,166,555,545,576,167,542,552,580,164,540,553,581,162,541,554,579,163,569,567,568,565,566,564,575,573,570,571,572,574,666,664,667,665,338,43,303,330,336,304,331,44,337,42,305,332,302,341,46,333,300,339,47,334,301,340,45,335,309,344,328,41,310,342,329,39,311,343,327,40,347,308,324,37,345,306,325,38,346,307,326,36,318,319,320,321,322,323,316,317,314,312,313,315,674,672,675,673 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#dc3952d3945a57ff89efbf9c91902a27e7bb606727f60175866197715516bbc5, 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 21:10:38 · history