Equation 677 Database

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Magma 302534f3cd86…

magma 302534f3cd86
Size
705
Isomorphism class hash
302534f3cd86757275dac8f6429be3ca748c738f03f58b5031eaee9538749c1a
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 15:18:34
Display reorder
660,482,400,18,494,304,19,483,495,305,401,17,402,484,496,306,485,21,403,497,307,486,22,404,498,308,487,20,405,499,309,480,16,398,492,302,481,14,399,493,303,479,15,397,491,301,12,476,394,488,298,13,477,395,489,299,11,478,396,490,300,684,673,682,679,75,231,103,376,270,104,73,377,268,229,105,230,74,378,269,71,102,227,379,273,72,100,228,380,271,70,101,226,381,272,81,94,237,374,265,79,95,235,375,266,80,96,236,373,267,97,77,233,370,264,98,78,234,371,262,99,76,232,372,263,664,665,668,672,470,518,112,316,239,113,471,317,240,519,114,520,472,318,238,473,115,521,319,242,474,116,522,320,243,475,117,523,321,241,468,110,516,314,245,469,111,517,315,246,467,109,515,313,244,106,464,512,310,248,107,465,513,311,249,108,466,514,312,247,675,683,680,685,613,615,29,619,614,30,620,627,622,623,31,631,628,635,630,637,32,639,643,638,645,33,647,651,646,652,34,655,659,654,597,27,599,603,598,604,28,607,611,606,589,26,591,595,590,23,565,566,569,568,24,572,575,579,574,25,580,583,587,582,702,701,703,704,436,189,143,292,424,144,437,293,425,187,142,188,438,294,426,439,146,185,295,427,440,147,186,296,428,441,145,184,297,429,434,149,180,290,422,435,150,178,291,423,433,148,179,289,421,152,430,183,286,418,153,431,181,287,419,151,432,182,288,420,690,692,693,689,506,458,125,171,256,126,507,169,257,459,124,460,508,170,258,509,128,461,167,259,510,129,462,168,260,511,127,463,166,261,504,123,456,177,254,505,121,457,175,255,503,122,455,176,253,119,500,452,173,250,120,501,453,174,251,118,502,454,172,252,661,662,670,667,364,8,210,450,57,208,365,451,55,9,209,10,366,449,56,367,213,7,448,48,368,211,5,561,560,369,212,6,562,563,362,205,2,443,52,363,206,3,444,53,361,207,0,442,54,204,358,1,446,51,202,359,35,447,49,203,360,4,445,50,696,695,691,694,328,554,93,530,62,91,329,531,63,555,92,556,330,532,61,331,89,557,533,58,332,90,558,534,59,333,88,559,535,60,326,84,552,528,68,327,82,553,529,69,325,83,551,527,67,87,322,548,524,64,85,323,549,525,65,86,324,550,526,66,686,674,676,687,616,617,216,612,618,214,624,621,626,625,215,633,632,629,634,640,219,641,636,642,648,217,649,644,650,656,218,657,653,658,600,222,601,596,602,608,220,609,605,610,592,221,593,588,594,225,570,571,564,567,223,576,577,573,578,224,584,585,581,586,698,700,697,699,542,138,285,340,412,283,543,341,413,136,284,137,544,342,414,545,281,141,343,415,546,282,139,344,416,547,280,140,345,417,540,276,133,338,410,541,274,134,339,411,539,275,135,337,409,279,536,132,334,406,277,537,130,335,407,278,538,131,336,408,663,666,671,669,165,352,198,388,38,196,163,389,36,353,197,354,164,390,37,161,201,355,391,41,162,199,356,392,39,160,200,357,393,40,156,193,350,386,44,154,194,351,387,42,155,195,349,385,43,192,159,346,382,47,190,157,347,383,45,191,158,348,384,46,678,681,688,677 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#11540e60a31227d97822464caf7bd085f23c491501101f6992da34196185b51e, 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 15:18:35 · history