Equation 677 Database

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Magma 8d25bcf03c2d…

magma 8d25bcf03c2d
Size
705
Isomorphism class hash
8d25bcf03c2ddd1d68fbbe2a883d3eda0a40a1db9130995b35b032c5865daefd
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 17:34:16
Display reorder
660,106,369,573,480,381,107,382,370,574,481,105,383,371,575,482,109,368,380,572,479,110,366,378,570,477,108,367,379,571,478,564,104,360,372,471,102,361,373,565,472,103,362,374,566,473,363,100,375,567,474,364,101,376,568,475,365,99,377,569,476,673,675,681,687,79,429,201,241,227,76,225,430,202,242,77,226,431,203,240,86,428,230,204,237,82,426,228,205,238,84,427,229,206,239,199,80,420,222,232,75,421,223,200,233,78,422,224,198,231,423,85,221,195,235,424,81,219,196,236,425,83,220,197,234,662,664,669,666,9,468,561,537,495,10,496,469,562,538,11,497,470,563,539,12,467,494,560,536,13,465,492,558,534,14,466,493,559,535,552,7,459,486,528,8,460,487,553,529,6,461,488,554,530,462,3,489,555,531,463,4,490,556,532,464,5,491,557,533,680,682,684,685,97,642,638,637,639,98,647,650,646,645,96,655,658,654,652,93,634,631,630,628,94,618,615,614,613,95,626,623,622,621,297,88,522,458,291,89,523,456,298,292,87,524,457,299,293,591,91,588,593,592,602,92,599,598,597,610,90,607,606,604,704,698,703,697,112,507,19,329,318,113,319,508,20,327,111,320,509,18,328,115,506,321,15,325,116,504,322,16,326,114,505,323,17,324,25,118,498,316,335,119,499,317,26,333,117,500,315,24,334,501,121,312,21,331,502,122,313,22,332,503,120,314,23,330,693,694,689,692,54,549,280,453,160,55,161,550,281,454,56,159,551,279,455,53,548,163,283,452,51,546,164,284,450,52,547,162,282,451,286,60,540,166,444,61,541,167,287,445,62,542,165,285,446,543,59,169,289,447,544,57,170,290,448,545,58,168,288,449,668,670,671,663,142,257,393,250,357,143,358,255,394,251,141,359,256,395,249,145,260,356,392,253,146,258,354,390,254,144,259,355,391,252,384,140,263,348,248,138,261,349,385,246,139,262,350,386,247,266,136,351,387,244,264,137,352,388,245,265,135,353,389,243,695,690,696,691,271,405,48,151,585,272,586,406,49,152,270,587,407,50,150,267,404,584,47,147,268,402,582,45,148,269,403,583,46,149,39,277,396,576,157,278,397,577,40,158,276,398,578,41,156,399,273,579,42,153,400,274,580,43,154,401,275,581,44,155,676,688,674,679,177,643,641,640,636,178,644,651,649,648,179,653,659,657,656,180,635,629,633,632,181,619,612,617,616,182,627,620,625,624,483,175,525,296,2,176,526,294,484,1,174,527,295,485,0,595,171,594,590,589,603,172,596,601,600,611,173,605,609,608,701,702,699,700,65,211,193,306,519,63,520,212,194,307,64,521,210,192,308,68,207,518,189,309,66,208,516,190,310,67,209,517,191,311,184,71,217,510,304,69,218,511,185,305,70,216,512,183,303,213,74,513,187,300,214,72,514,188,301,215,73,515,186,302,672,665,661,667,132,417,34,441,343,133,344,418,35,442,134,342,419,33,443,131,416,346,37,440,129,414,347,38,438,130,415,345,36,439,32,123,408,341,432,124,409,339,30,433,125,410,340,31,434,411,126,337,28,435,412,127,338,29,436,413,128,336,27,437,677,686,678,683 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#58f4898eb0f0372a4c749060353e7621900aa789e1d944064f9989e660cee0fd, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:34:17 · history