Equation 677 Database

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Magma d7c83915205c…

magma d7c83915205c
Size
720
Isomorphism class hash
d7c83915205c3b2c40dc6e0c1fe2a72f6acc1071baf37e01dc59ad9c9ead3cc9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 09:43:44
Display reorder
513,514,515,516,517,518,519,520,521,522,523,524,510,511,512,719,157,130,141,158,131,142,159,132,143,160,133,144,161,134,145,162,120,146,163,121,147,164,122,148,150,123,149,151,124,135,152,125,136,153,126,137,154,127,138,155,128,139,156,129,140,113,105,106,107,108,109,110,111,112,115,116,117,118,119,114,690,688,689,687,367,340,352,368,341,353,369,342,354,370,343,355,371,344,356,372,330,357,373,331,358,374,332,359,360,333,345,361,334,346,362,335,347,363,336,348,364,337,349,365,338,350,366,339,351,321,328,329,315,316,317,318,319,320,323,324,325,326,327,322,681,682,680,679,39,169,182,40,170,183,41,171,184,42,172,185,43,173,186,44,174,187,30,175,188,31,176,189,32,177,190,33,178,191,34,179,192,35,165,193,36,166,194,37,167,180,38,168,181,661,662,663,664,665,666,667,668,669,670,660,673,674,672,671,700,702,699,701,550,576,534,551,577,535,552,578,536,553,579,537,554,580,538,540,581,539,541,582,525,542,583,526,543,584,527,544,570,528,545,571,529,546,572,530,547,573,531,548,574,532,549,575,533,559,566,567,568,569,555,556,557,558,561,562,563,564,565,560,716,717,715,718,451,490,436,452,491,437,453,492,438,454,493,439,455,494,440,456,480,441,457,481,442,458,482,443,459,483,444,460,484,445,461,485,446,462,486,447,463,487,448,464,488,449,450,489,435,473,465,466,467,468,469,470,471,472,475,476,477,478,479,474,706,703,705,704,271,314,257,272,300,258,273,301,259,274,302,260,275,303,261,276,304,262,277,305,263,278,306,264,279,307,265,280,308,266,281,309,267,282,310,268,283,311,269,284,312,255,270,313,256,295,287,288,289,290,291,292,293,294,297,298,299,285,286,296,678,676,677,675,495,3,596,496,4,597,497,5,598,498,6,599,499,7,585,500,8,586,501,9,587,502,10,588,503,11,589,504,12,590,505,13,591,506,14,592,507,1,593,508,0,594,509,2,595,26,18,19,20,21,22,23,24,25,28,29,15,16,17,27,709,708,710,707,206,231,243,207,232,244,208,233,245,209,234,246,195,235,247,196,236,248,197,237,249,198,238,250,199,239,251,200,225,252,201,226,253,202,227,254,203,228,240,204,229,241,205,230,242,213,220,221,222,223,224,210,211,212,215,216,217,218,219,214,696,698,695,697,631,606,617,632,607,618,633,608,619,634,609,620,635,610,621,636,611,622,637,612,623,638,613,624,639,614,625,640,600,626,641,601,627,642,602,628,643,603,629,644,604,615,630,605,616,653,645,646,647,648,649,650,651,652,655,656,657,658,659,654,712,713,714,711,422,395,407,423,396,408,424,397,409,425,398,410,426,399,411,427,400,412,428,401,413,429,402,414,430,403,415,431,404,416,432,390,417,433,391,418,434,392,419,420,393,405,421,394,406,378,385,386,387,388,389,375,376,377,380,381,382,383,384,379,685,684,686,683,62,102,47,63,103,48,64,104,49,65,90,50,66,91,51,67,92,52,68,93,53,69,94,54,70,95,55,71,96,56,72,97,57,73,98,58,74,99,59,60,100,45,61,101,46,84,76,77,78,79,80,81,82,83,86,87,88,89,75,85,691,693,692,694 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 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#7c9587bb487c7f78877b32bd3c6516b6b04394ef6d405ed5492c6ed5480f025c, M = {0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 45, 49, 53, 57, 75} 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 2026-10-08 09:43:45 · history