Equation 677 Database

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Magma 95baed928354…

magma 95baed928354
Size
705
Isomorphism class hash
95baed928354eef5f961ad1c43b9f821da7489581351770407b8b071dbca57d4
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 19:51:15
Display reorder
660,507,522,312,492,133,508,523,134,313,493,509,524,132,314,494,521,506,136,311,491,519,504,137,309,489,520,505,135,310,490,131,513,318,498,483,129,514,319,499,484,130,515,320,500,485,516,127,317,501,486,517,128,315,502,487,518,126,316,503,488,682,683,681,685,230,185,15,63,245,228,183,243,16,64,229,184,244,17,65,181,233,241,18,66,182,231,242,19,67,180,232,240,20,68,236,176,21,225,69,234,174,22,226,70,235,175,23,227,71,179,239,24,224,72,177,237,25,222,73,178,238,26,223,74,664,667,663,671,268,561,329,252,13,269,562,14,327,253,267,563,12,328,254,560,264,9,332,255,558,265,10,330,256,559,266,11,331,257,4,552,324,259,250,5,553,325,260,251,3,554,326,258,249,555,7,323,262,246,556,8,321,263,247,557,6,322,261,248,679,686,687,674,638,637,82,642,640,646,645,648,83,650,654,653,656,81,658,629,630,632,85,634,613,614,616,86,618,621,622,624,84,626,480,87,80,284,510,481,88,78,282,511,482,89,79,283,512,588,590,76,592,593,596,600,77,598,602,604,608,75,606,610,703,698,700,704,390,477,102,138,307,391,478,308,103,139,392,479,306,104,140,476,389,303,105,141,474,387,304,106,142,475,388,305,107,143,298,468,108,381,144,299,469,109,382,145,297,470,110,383,146,471,301,111,384,147,472,302,112,385,148,473,300,113,386,149,691,692,689,693,281,549,96,343,573,279,550,574,97,344,280,551,575,98,342,548,277,572,99,339,546,278,570,100,340,547,276,571,101,341,564,540,94,272,334,565,541,95,270,335,566,542,93,271,333,543,567,90,275,337,544,568,91,273,338,545,569,92,274,336,665,670,669,672,431,153,30,43,360,429,154,361,31,44,430,155,362,32,42,152,434,359,29,39,150,432,357,27,40,151,433,358,28,41,366,159,36,437,49,367,160,37,435,50,368,161,38,436,48,158,365,35,440,45,156,363,33,438,46,157,364,34,439,47,694,695,696,690,378,585,55,450,534,379,586,535,56,451,380,587,536,54,452,584,377,533,51,449,582,375,531,52,447,583,376,532,53,448,525,576,61,369,441,526,577,62,370,442,527,578,60,371,443,579,528,57,372,444,580,529,58,373,445,581,530,59,374,446,673,688,677,684,641,639,173,636,643,649,647,651,171,644,657,655,659,172,652,631,633,635,169,628,615,617,619,170,612,623,625,627,168,620,537,467,164,495,1,538,465,162,496,0,539,466,163,497,2,594,595,167,591,589,599,603,165,601,597,607,611,166,609,605,699,697,702,701,414,209,292,214,194,415,207,192,293,215,416,208,193,291,213,205,413,197,295,210,206,411,195,296,211,204,412,196,294,212,189,200,290,405,220,190,198,288,406,221,191,199,289,407,219,203,188,286,408,216,201,186,287,409,217,202,187,285,410,218,662,666,668,661,462,426,117,402,355,463,427,356,118,403,464,428,354,119,404,425,461,351,116,401,423,459,352,114,399,424,460,353,115,400,346,417,123,453,393,347,418,124,454,394,345,419,125,455,395,420,349,122,456,396,421,350,120,457,397,422,348,121,458,398,678,676,675,680 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#b24873ef385d9876d07add1b0ccd1e5b9965acff1b69e8225210d446f480d74b, 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 19:51:16 · history