Equation 677 Database

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Magma 1344d63fa76d…

magma 1344d63fa76d
Size
705
Isomorphism class hash
1344d63fa76da553f1305335a97265dd75aa4e0a8d2bc57b5977082521eeacda
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 18:25:14
Display reorder
660,325,457,553,421,493,326,494,458,554,422,456,492,327,552,420,496,324,460,556,424,497,322,461,557,425,495,323,459,555,423,316,499,463,559,427,500,464,560,317,428,498,462,558,318,426,466,502,562,319,430,467,503,563,320,431,465,501,561,321,429,668,665,666,667,112,469,565,28,505,113,506,470,566,29,468,504,114,564,27,508,115,472,568,24,509,116,473,569,25,507,117,471,567,26,118,511,475,571,34,512,476,572,119,35,510,474,570,120,33,478,514,574,121,30,479,515,575,122,31,477,513,573,123,32,691,690,686,688,162,609,328,355,343,160,344,610,329,356,608,345,161,330,357,342,165,612,331,354,340,163,613,332,352,341,164,611,333,353,168,349,615,334,361,350,616,335,166,362,351,614,336,167,363,618,348,337,171,360,619,346,338,169,358,617,347,339,170,359,662,670,672,671,50,377,481,433,232,48,233,378,482,434,376,234,49,480,432,235,53,380,484,436,236,51,381,485,437,237,52,379,483,435,56,238,383,487,439,239,384,488,54,440,240,382,486,55,438,386,241,490,59,442,387,242,491,57,443,385,243,489,58,441,678,676,674,681,254,397,303,589,305,255,306,398,301,590,396,304,253,302,588,308,250,400,299,592,309,251,401,300,593,307,252,399,298,591,245,311,403,294,595,312,404,292,246,596,310,402,293,244,594,406,314,297,248,598,407,315,295,249,599,405,313,296,247,597,661,669,664,663,153,621,529,577,365,151,366,622,530,578,620,364,152,528,576,368,149,624,532,580,369,150,625,533,581,367,148,623,531,579,159,371,627,535,583,372,628,536,157,584,370,626,534,158,582,630,374,538,155,586,631,375,539,156,587,629,373,537,154,585,697,698,700,694,66,85,601,392,78,67,79,86,602,393,87,77,68,600,391,74,69,84,604,388,75,70,82,605,389,76,71,83,603,390,64,72,80,607,395,647,645,646,65,644,73,81,606,63,394,654,653,655,60,652,658,657,659,61,656,650,648,651,62,649,704,701,703,702,89,256,227,445,517,90,518,257,228,446,258,516,88,226,444,520,92,259,230,448,521,93,260,231,449,519,91,261,229,447,95,523,262,225,451,524,263,223,96,452,522,264,224,94,450,265,526,221,98,454,266,527,222,99,455,267,525,220,97,453,699,695,693,696,11,13,268,143,285,9,283,14,269,144,12,284,10,270,142,281,7,16,271,146,282,8,17,272,147,280,6,15,273,145,2,291,19,274,141,289,20,275,1,139,290,18,276,0,140,22,287,277,5,137,23,288,278,3,138,21,286,279,4,136,677,680,682,684,39,541,100,633,409,40,410,542,101,634,540,408,41,102,632,412,38,544,103,636,413,36,545,104,637,411,37,543,105,635,45,415,547,106,639,416,548,107,46,640,414,546,108,47,638,550,418,109,44,642,551,419,110,42,643,549,417,111,43,641,673,683,679,675,124,200,183,218,184,125,185,201,181,219,199,186,126,182,217,187,127,196,179,214,188,128,197,180,215,189,129,198,178,216,130,190,206,174,209,191,207,172,131,210,192,205,173,132,208,202,193,177,133,212,203,194,175,134,213,204,195,176,135,211,685,692,687,689 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#82fe73547f12a148ba897be501ddca2fd72765d56930c9a3792aacda34cfdc1d, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 18:25:15 · history