Equation 677 Database

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Magma 3df4e7efa5d5…

magma 3df4e7efa5d5
Size
705
Isomorphism class hash
3df4e7efa5d53ee995c9071a1bfa54ed855670d7f01eb64f36967cbe7c7a2854
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 15:04:18
Display reorder
660,378,21,155,573,414,379,22,153,574,415,380,23,154,575,416,377,20,151,572,413,375,18,152,570,411,19,376,150,571,412,146,369,12,564,405,144,370,13,565,406,145,371,14,566,407,372,149,15,567,408,373,147,16,568,409,374,148,17,569,410,687,678,680,675,318,243,339,307,271,319,244,340,308,272,320,245,341,306,270,321,246,338,310,274,322,247,336,311,275,248,323,337,309,273,330,324,249,313,277,331,325,250,314,278,332,326,251,312,276,327,333,252,316,280,328,334,253,317,281,329,335,254,315,279,663,662,664,669,477,91,181,453,537,478,92,182,454,538,479,90,180,455,539,476,94,184,452,536,474,95,185,450,534,93,475,183,451,535,187,468,89,444,528,188,469,87,445,529,186,470,88,446,530,471,190,85,447,531,472,191,86,448,532,473,189,84,449,533,681,684,685,682,638,6,639,636,642,646,7,647,645,650,654,8,655,653,658,630,9,631,629,634,614,10,615,613,618,11,622,623,621,626,203,199,4,197,366,201,200,5,195,367,202,198,3,196,368,589,590,1,592,593,598,599,0,596,602,606,607,2,604,610,704,697,698,703,291,218,351,160,501,292,216,352,161,502,293,217,353,159,503,290,221,350,156,500,288,219,348,157,498,220,289,349,158,499,342,282,224,166,492,343,283,222,167,493,344,284,223,165,494,285,345,227,162,495,286,346,225,163,496,287,347,226,164,497,689,693,692,690,549,124,59,489,465,550,125,57,490,466,551,123,58,491,467,548,120,55,488,464,546,121,56,486,462,122,547,54,487,463,50,540,130,480,456,48,541,131,481,457,49,542,129,482,458,543,53,126,483,459,544,51,127,484,460,545,52,128,485,461,670,668,661,672,303,255,236,61,178,304,256,234,62,179,305,257,235,60,177,302,258,239,64,174,300,259,237,65,175,260,301,238,63,176,231,294,261,67,169,232,295,262,68,170,233,296,263,66,168,297,230,264,70,172,298,228,265,71,173,299,229,266,69,171,694,695,696,691,561,80,426,390,585,562,78,427,391,586,563,79,428,392,587,560,83,425,389,584,558,81,423,387,582,82,559,424,388,583,417,552,75,381,576,418,553,76,382,577,419,554,77,383,578,555,420,74,384,579,556,421,72,385,580,557,422,73,386,581,676,688,679,686,641,98,643,637,640,649,96,651,644,648,657,97,659,652,656,633,101,635,628,632,617,99,619,612,616,100,625,627,620,624,431,268,104,192,241,429,269,102,193,242,430,267,103,194,240,594,595,107,588,591,601,603,105,597,600,609,611,106,605,608,702,700,699,701,525,44,363,441,213,526,42,364,442,214,527,43,365,443,215,524,47,362,440,212,522,45,360,438,210,46,523,361,439,211,354,516,39,432,204,355,517,40,433,205,356,518,41,434,206,519,357,38,435,207,520,358,36,436,208,521,359,37,437,209,667,666,665,671,402,34,513,139,116,403,35,514,140,114,404,33,515,138,115,401,30,512,142,119,399,31,510,143,117,32,400,511,141,118,504,393,25,137,111,505,394,26,135,112,506,395,24,136,113,396,507,28,133,110,397,508,29,134,108,398,509,27,132,109,673,674,683,677 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#01253a2afae29ad04ad4e5938d81c583acd3aeb3895dbf3461a9c0b97e71e908, 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 15:04:25 · history