Equation 677 Database

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Magma 4e85a949c16a…

magma 4e85a949c16a
Size
705
Isomorphism class hash
4e85a949c16aea4ac9ade953231990de1a5ff7459c9866ae0cd047a7c2b0499b
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 16:52:35
Display reorder
660,130,611,607,608,610,131,628,631,627,630,129,648,651,647,650,126,591,588,587,590,127,551,548,547,550,128,571,568,567,570,427,431,121,428,430,445,449,122,446,448,467,471,120,468,470,491,487,124,488,490,511,507,125,508,510,531,527,123,528,530,699,695,687,698,88,617,616,601,602,89,621,637,636,622,87,641,657,656,642,84,597,580,596,582,85,557,541,556,542,86,577,561,576,562,436,437,94,421,422,454,455,95,442,441,476,477,93,462,461,497,496,90,481,482,517,516,91,501,502,537,536,92,521,522,697,704,685,690,14,10,113,309,101,12,310,11,111,99,13,311,9,112,100,17,6,308,109,97,15,7,306,110,98,16,8,307,108,96,119,0,20,300,107,117,2,18,301,105,118,1,19,302,106,4,115,23,303,103,5,116,21,304,104,3,114,22,305,102,676,665,679,672,155,270,232,167,417,153,165,271,233,418,154,166,272,231,419,151,273,163,228,416,152,274,164,229,414,150,275,162,230,415,238,268,146,158,408,239,269,144,156,409,237,267,145,157,410,264,234,149,161,411,265,235,147,159,412,266,236,148,160,413,668,682,684,669,76,604,615,603,600,77,623,624,635,620,75,643,644,655,640,72,584,583,595,581,73,544,543,555,540,74,564,563,575,560,435,424,82,423,420,453,459,83,458,457,475,464,81,463,460,484,495,78,483,480,504,515,79,503,500,524,535,80,523,520,689,688,692,702,37,614,619,612,605,38,632,634,639,625,36,652,654,659,645,40,594,592,599,585,41,554,552,559,545,39,574,572,579,565,439,434,43,432,425,440,452,44,450,443,479,474,42,472,465,494,499,46,492,485,514,519,47,512,505,534,539,45,532,525,700,691,701,694,210,618,609,606,613,211,626,638,629,633,212,646,658,649,653,213,598,586,589,593,214,558,546,549,553,215,578,566,569,573,429,438,208,426,433,447,456,209,444,451,469,478,207,466,473,498,489,204,486,493,518,509,205,506,513,538,529,206,526,533,696,686,693,703,58,357,261,285,251,59,286,358,262,249,57,287,359,263,250,54,356,284,260,247,55,354,282,258,248,56,355,283,259,246,252,348,49,276,242,253,349,50,277,240,254,350,48,278,241,351,255,52,279,245,352,256,53,280,243,353,257,51,281,244,661,663,662,674,219,193,188,405,134,220,406,194,186,132,221,407,192,187,133,218,196,404,191,137,216,197,402,189,135,217,195,403,190,136,183,199,225,396,140,184,200,226,397,138,185,198,227,398,139,202,182,224,399,143,203,180,222,400,141,201,181,223,401,142,680,683,677,670,168,369,345,321,297,169,322,370,346,298,170,323,371,347,299,171,368,320,344,296,172,366,318,342,294,173,367,319,343,295,336,360,174,312,288,337,361,175,313,289,338,362,176,314,290,363,339,177,315,291,364,340,178,316,292,365,341,179,317,293,673,666,664,675,66,393,34,381,333,67,382,394,35,334,68,383,395,33,335,69,392,380,30,332,70,390,378,31,330,71,391,379,32,331,25,384,64,372,324,26,385,65,373,325,24,386,63,374,326,387,28,60,375,327,388,29,61,376,328,389,27,62,377,329,671,678,667,681 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#458b3cfe489c9903ffdf95802569f7fced83cfa9f913419e94bc2fd3ec4c05bf, 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 16:52:35 · history