Equation 677 Database

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Magma 4c70c2b7cb50…

magma 4c70c2b7cb50
Size
705
Isomorphism class hash
4c70c2b7cb505a2cfc5bd64e1749d791f308eaee80b80f57ad9ddfa14dfe9f42
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 20:33:38
Display reorder
660,221,409,422,381,392,219,410,423,379,393,220,411,421,380,391,224,408,418,377,388,222,406,419,378,389,223,407,420,376,390,216,400,413,387,398,217,401,414,385,399,218,402,412,386,397,403,215,416,383,394,404,213,417,384,395,405,214,415,382,396,685,686,688,687,492,299,175,126,291,490,297,176,127,292,491,298,174,128,293,495,302,178,129,294,493,300,179,130,295,494,301,177,131,296,487,305,173,124,289,488,303,171,125,290,489,304,172,123,288,308,486,169,120,285,306,484,170,121,286,307,485,168,122,287,701,702,704,703,18,598,604,375,212,19,599,605,373,210,20,600,606,374,211,21,601,607,371,208,22,602,608,372,209,23,603,609,370,207,16,596,610,366,203,17,597,611,364,201,15,595,612,365,202,592,12,613,369,206,593,13,614,367,204,594,14,615,368,205,670,669,672,671,501,149,4,316,135,499,147,5,317,136,500,148,6,315,137,497,145,10,319,134,498,146,3,320,132,496,144,9,318,133,507,155,11,314,141,505,153,7,312,142,506,154,8,313,143,151,503,1,310,140,152,504,0,311,138,150,502,2,309,139,680,677,679,678,509,158,107,111,327,510,156,105,112,328,508,157,106,113,329,512,161,103,110,330,513,159,104,108,331,511,160,102,109,332,515,164,98,117,325,516,162,96,118,326,514,163,97,119,324,167,518,101,116,321,165,519,99,114,322,166,517,100,115,323,689,690,691,692,348,565,579,537,548,349,566,577,535,549,350,567,578,536,547,347,564,575,533,544,345,562,576,534,545,346,563,574,532,546,354,556,570,543,554,355,557,568,541,555,356,558,569,542,553,559,353,573,539,550,560,351,571,540,551,561,352,572,538,552,697,698,700,699,68,624,639,81,94,66,622,637,82,95,67,623,638,83,93,71,627,635,80,90,69,625,636,78,91,70,626,634,79,92,63,619,630,72,85,64,620,628,73,86,65,621,629,74,84,618,62,633,75,88,616,60,631,76,89,617,61,632,77,87,661,662,664,663,427,233,248,254,266,428,231,246,252,264,429,232,247,253,265,426,236,244,250,262,424,234,245,251,263,425,235,243,249,261,433,228,239,260,272,434,229,237,258,270,435,230,238,259,271,227,432,242,256,268,225,430,240,257,269,226,431,241,255,267,682,681,684,683,591,358,195,180,188,589,359,196,181,186,590,360,197,182,187,587,361,198,183,191,588,362,199,184,189,586,363,200,185,190,582,647,646,645,644,580,357,194,193,192,581,642,641,640,643,659,585,657,656,658,651,583,648,649,650,655,584,652,653,654,693,694,696,695,52,46,47,528,342,53,42,43,526,343,51,44,45,527,344,48,38,39,531,341,49,40,41,529,339,50,36,37,530,340,58,28,29,523,333,59,25,24,524,334,57,27,26,525,335,35,54,34,522,336,30,55,31,520,337,33,56,32,521,338,666,665,668,667,284,453,463,475,441,282,451,464,476,439,283,452,465,477,440,280,449,462,474,437,281,450,460,472,438,279,448,461,473,436,275,459,469,481,447,273,457,470,482,445,274,458,471,483,446,455,278,468,480,443,456,276,466,478,444,454,277,467,479,442,674,673,676,675 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, 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 20:33:39 · history