Equation 677 Database

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Magma afd22e491c39…

magma afd22e491c39
Size
705
Isomorphism class hash
afd22e491c3974da10e3a2df2f9b73328eab1d067137a7cd4676f7871b9d88d0
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 17:40:10
Display reorder
704,348,387,373,524,349,522,388,374,350,523,389,372,527,351,386,376,525,352,384,377,526,353,385,375,379,519,393,354,380,520,394,355,378,521,395,356,518,382,392,357,516,383,390,358,517,381,391,359,368,366,367,371,369,370,363,364,361,362,360,365,675,673,674,672,186,177,162,140,187,138,178,163,188,139,179,164,143,189,176,165,141,190,174,166,142,191,175,167,160,135,168,184,161,136,169,185,159,137,170,183,134,156,171,180,132,157,172,181,133,158,173,182,197,195,196,193,194,192,203,201,198,199,200,202,664,666,665,667,556,541,531,398,557,396,542,532,555,397,540,533,401,552,544,530,399,553,545,528,400,554,543,529,537,404,547,562,538,402,548,563,539,403,546,561,407,536,550,558,405,534,551,559,406,535,549,560,648,649,650,651,652,653,654,655,658,656,657,659,686,684,685,687,100,84,123,77,101,75,85,124,99,76,86,125,73,96,87,122,74,97,88,120,72,98,89,121,129,83,90,106,130,81,91,107,131,82,92,105,79,128,93,102,80,126,94,103,78,127,95,104,117,118,119,116,114,115,108,109,113,111,112,110,701,703,700,702,50,241,618,647,48,645,242,619,49,646,240,620,643,53,244,621,644,51,245,622,642,52,243,623,616,638,247,56,617,636,248,54,615,637,246,55,641,612,250,59,639,613,251,57,640,614,249,58,43,44,42,46,47,45,41,39,36,37,38,40,688,690,689,691,427,466,450,13,428,14,467,451,426,12,465,452,16,430,462,453,17,431,463,454,15,429,464,455,448,19,457,425,449,20,458,423,447,18,456,424,22,444,460,421,23,445,461,422,21,446,459,420,435,436,437,434,432,433,441,442,439,440,438,443,662,661,663,660,265,255,289,1,266,0,256,290,264,2,257,288,3,268,254,292,4,269,252,293,5,267,253,291,295,6,261,271,296,7,262,272,294,8,263,270,9,298,260,274,10,299,258,275,11,297,259,273,284,282,283,287,285,286,279,280,277,278,276,281,694,693,695,692,608,597,582,411,606,412,598,583,607,413,599,584,410,611,596,585,408,609,594,586,409,610,595,587,580,417,588,603,581,418,589,604,579,419,590,605,416,576,591,602,414,577,592,600,415,578,593,601,568,569,567,564,565,566,574,575,572,570,571,573,682,683,681,680,303,337,328,155,304,153,338,329,305,154,336,327,151,302,340,324,152,300,341,325,150,301,339,326,334,146,343,309,335,144,344,310,333,145,342,311,149,330,346,308,147,331,347,306,148,332,345,307,323,321,322,319,320,318,314,312,316,317,315,313,696,698,699,697,223,213,631,25,224,26,214,632,222,24,215,630,28,226,212,634,29,227,210,635,27,225,211,633,629,31,204,221,627,32,205,219,628,30,206,220,34,625,207,217,35,626,208,218,33,624,209,216,231,232,233,230,228,229,237,238,235,236,234,239,671,668,670,669,495,482,472,71,496,69,480,473,497,70,481,471,67,494,485,468,68,492,483,469,66,493,484,470,478,62,488,501,479,60,486,502,477,61,487,503,65,474,491,500,63,475,489,498,64,476,490,499,514,515,513,510,511,512,505,506,507,508,509,504,676,678,677,679 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#5e80e1c2dc82944cee69cb7089d21c45f5ab65bc382c5d130a060fbb3f31d2ae, 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 17:40:13 · history