Equation 677 Database

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Magma 1f28603f37f7…

magma 1f28603f37f7
Size
705
Isomorphism class hash
1f28603f37f774dcee24b9ce30ef8523697d2f180e86cc486d8e890ba2c77041
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 20:41:01
Display reorder
660,232,270,592,244,255,230,271,590,242,256,231,269,591,243,254,266,235,595,247,258,267,233,593,245,259,268,234,594,246,257,587,276,250,238,261,588,277,248,236,262,589,275,249,237,260,272,586,253,241,264,273,584,251,239,265,274,585,252,240,263,687,688,686,685,79,352,378,362,340,77,350,379,363,338,78,351,377,364,339,355,75,374,365,343,353,76,375,366,341,354,74,376,367,342,384,358,368,85,346,385,356,369,83,344,383,357,370,84,345,361,380,371,81,349,359,381,372,82,347,360,382,373,80,348,703,704,701,702,225,537,569,553,572,226,538,570,551,573,224,536,571,552,574,540,228,568,549,575,541,229,566,550,576,539,227,567,548,577,560,543,559,223,578,561,544,557,221,579,562,542,558,222,580,546,563,555,219,581,547,564,556,220,582,545,565,554,218,583,671,672,670,669,101,399,424,413,389,102,400,422,414,390,103,398,423,415,391,402,100,427,412,388,403,98,425,410,386,401,99,426,411,387,430,405,419,107,395,428,406,420,108,396,429,404,421,109,397,408,433,418,106,394,409,431,416,104,392,407,432,417,105,393,679,680,678,677,71,450,479,463,438,72,451,480,461,439,73,449,481,462,437,446,70,478,459,434,447,68,476,460,435,448,69,477,458,436,470,456,469,62,444,471,457,467,63,445,472,455,468,64,443,452,473,465,65,440,453,474,466,66,441,454,475,464,67,442,692,691,690,689,502,160,185,171,196,500,158,186,172,194,501,159,187,170,195,163,505,184,174,199,161,503,182,175,197,162,504,183,173,198,191,166,177,497,202,192,164,178,498,200,193,165,176,499,201,169,190,180,496,205,167,188,181,494,203,168,189,179,495,204,699,700,698,697,59,9,32,21,48,60,10,33,22,49,61,8,34,20,47,12,58,35,24,44,13,56,36,25,45,11,57,37,23,46,30,7,19,50,39,31,5,17,51,40,29,6,18,52,38,3,26,15,53,42,4,27,16,54,43,2,28,14,55,41,663,664,662,661,287,610,634,622,598,288,608,632,620,596,289,609,633,621,597,613,286,637,625,601,611,284,635,623,599,612,285,636,624,600,640,616,628,278,604,638,614,626,279,602,639,615,627,280,603,619,643,631,281,607,617,641,629,282,605,618,642,630,283,606,682,683,684,681,207,659,657,656,658,208,651,648,649,650,206,655,653,652,654,528,210,0,513,520,646,211,645,644,647,529,209,1,512,521,515,534,511,213,523,516,535,509,214,524,514,533,510,212,522,530,518,507,216,526,531,519,508,217,527,532,517,506,215,525,695,696,693,694,486,143,114,147,127,487,144,115,148,125,485,145,113,146,126,142,482,110,150,123,140,483,111,151,124,141,484,112,149,122,120,134,153,492,133,121,135,154,493,131,119,136,152,491,132,137,116,156,488,129,138,117,157,489,130,139,118,155,490,128,667,668,665,666,96,317,293,327,302,97,318,294,328,303,95,319,295,326,304,316,92,292,330,305,314,93,290,331,306,315,94,291,329,307,299,323,333,87,308,300,324,334,88,309,301,325,332,86,310,322,298,336,90,311,320,296,337,91,312,321,297,335,89,313,675,676,673,674 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#cb899e6f30effddffe30366e2e9dc963aa0ce854a3a9ff04422e3e195000d2a8, 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 20:41:02 · history