Equation 677 Database

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Magma 4b0b5a0eebdb…

magma 4b0b5a0eebdb
Size
705
Isomorphism class hash
4b0b5a0eebdb9ab48b159adaa2238791b5714fd79db8d394cc6280186556fbcb
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 17:23:43
Display reorder
660,454,574,478,310,550,455,575,311,479,551,312,573,453,477,549,450,570,313,474,546,451,571,314,475,547,452,572,315,476,548,565,445,308,469,541,566,446,309,470,542,564,444,307,468,540,448,568,304,472,544,449,569,305,473,545,447,567,306,471,543,679,681,685,687,130,145,110,345,490,128,143,343,111,491,344,144,129,112,489,133,141,341,113,486,131,142,342,114,487,132,140,340,115,488,151,136,351,108,481,149,134,349,109,482,150,135,350,107,480,139,147,347,104,484,137,148,348,105,485,138,146,346,106,483,670,662,667,672,362,378,526,34,426,363,379,35,527,427,33,377,361,525,425,358,374,37,522,422,359,375,38,523,423,360,376,36,524,424,369,353,32,517,417,370,354,30,518,418,368,352,31,516,416,356,372,28,520,420,357,373,29,521,421,355,371,27,519,419,673,683,677,675,650,644,648,4,649,658,653,5,656,657,3,636,642,640,641,618,612,7,616,617,626,620,8,624,625,634,629,6,632,633,2,577,10,367,441,1,578,11,365,442,0,576,9,366,440,599,596,13,600,601,610,605,14,608,609,579,103,12,364,443,704,697,699,703,326,52,389,170,402,327,53,171,390,403,169,51,325,391,401,322,55,166,388,398,323,56,167,386,399,324,54,168,387,400,58,317,161,380,393,59,318,162,381,394,57,316,160,382,392,320,61,164,383,396,321,62,165,384,397,319,60,163,385,395,690,694,691,689,538,83,17,221,276,539,81,222,15,274,220,82,537,16,275,534,86,224,20,279,535,84,225,18,277,536,85,223,19,278,78,529,227,23,271,79,530,228,21,272,80,528,226,22,273,532,77,230,26,270,533,75,231,24,268,531,76,229,25,269,669,664,661,666,196,252,178,88,189,197,250,89,179,187,87,251,198,180,188,199,255,91,181,185,200,253,92,182,186,201,254,90,183,184,247,202,94,176,195,248,203,95,177,193,249,204,93,175,194,205,246,97,172,191,206,244,98,173,192,207,245,96,174,190,692,695,696,693,562,466,594,266,215,563,467,267,595,216,265,465,561,593,214,558,462,262,590,218,559,463,263,591,219,560,464,264,592,217,457,553,257,585,213,458,554,258,586,211,456,552,256,584,212,556,460,260,588,209,557,461,261,589,210,555,459,259,587,208,686,688,674,680,651,646,647,40,645,659,654,41,655,652,39,638,643,639,637,619,614,43,615,613,627,622,44,623,621,635,630,42,631,628,153,581,46,157,102,154,582,47,158,100,155,580,45,156,101,603,602,49,598,597,611,606,50,607,604,583,152,48,159,99,702,698,700,701,514,414,121,338,438,515,415,339,119,439,337,413,513,120,437,510,410,334,117,434,511,411,335,118,435,512,412,336,116,436,405,505,329,127,429,406,506,330,125,430,404,504,328,126,428,508,408,332,123,432,509,409,333,124,433,507,407,331,122,431,668,671,665,663,74,286,295,241,502,72,287,242,296,503,243,288,73,297,501,70,289,240,294,498,71,290,238,292,499,69,291,239,293,500,284,65,232,301,493,285,63,233,302,494,283,64,234,303,492,68,280,235,300,496,66,281,236,298,497,67,282,237,299,495,678,676,682,684 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#51b008b28ab03bd312921cf92cf8265fda62df0fbe14e18f3974b5c43c79b0a4, 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 17:23:45 · history