Equation 677 Database

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Magma aa7ec9a28707…

magma aa7ec9a28707
Size
705
Isomorphism class hash
aa7ec9a2870795fd37e722646ec17f0d335561df3716bb97ac92d17585fb888f
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 19:17:23
Display reorder
660,526,512,306,342,440,340,524,510,304,438,341,525,511,305,439,345,529,515,309,443,343,527,513,307,441,344,528,514,308,442,521,507,301,337,435,522,508,302,338,436,523,509,303,339,437,520,506,300,336,434,518,504,298,334,432,519,505,299,335,433,682,679,683,675,464,224,270,189,226,187,462,225,268,227,188,463,223,269,228,185,467,220,273,229,186,465,221,271,230,184,466,222,272,231,459,215,265,180,232,460,216,266,178,233,461,214,267,179,234,458,218,264,183,235,456,219,262,181,236,457,217,263,182,237,669,672,667,663,488,550,282,246,59,244,486,548,280,57,245,487,549,281,58,249,491,553,285,55,247,489,551,283,56,248,490,552,284,54,483,545,277,241,50,484,546,278,242,48,485,547,279,243,49,482,544,276,240,53,480,542,274,238,51,481,543,275,239,52,685,687,680,673,629,630,628,203,635,204,613,614,612,619,202,621,622,620,627,206,653,654,652,659,207,637,638,636,643,205,645,646,644,651,589,590,588,209,595,596,598,597,210,603,604,606,605,208,611,580,582,581,212,584,120,125,122,213,578,121,124,123,211,579,701,700,704,698,354,378,366,196,146,197,352,376,364,147,198,353,377,365,145,199,357,381,369,142,200,355,379,367,143,201,356,380,368,144,349,373,361,194,152,350,374,362,195,153,351,375,363,193,151,348,372,360,190,148,346,370,358,191,149,347,371,359,192,150,692,696,690,691,452,258,294,21,43,22,450,256,292,44,23,451,257,293,42,20,455,261,297,46,18,453,259,295,47,19,454,260,296,45,447,253,289,12,41,448,254,290,13,39,449,255,291,14,40,446,252,288,15,37,444,250,286,16,38,445,251,287,17,36,662,661,666,664,141,106,402,70,426,71,139,107,400,424,69,140,105,401,425,66,137,102,405,429,67,138,103,403,427,68,136,104,404,428,132,97,397,61,421,130,98,398,62,422,131,96,399,60,423,135,100,396,64,420,133,101,394,65,418,134,99,395,63,419,689,694,695,693,34,330,500,110,562,108,35,328,498,560,109,33,329,499,561,113,30,333,503,565,111,31,331,501,563,112,32,332,502,564,25,325,495,116,557,26,326,496,114,558,24,327,497,115,559,28,324,494,119,556,29,322,492,117,554,27,323,493,118,555,676,686,684,681,632,633,634,0,631,2,616,617,618,615,1,624,625,626,623,4,656,657,658,655,5,640,641,642,639,3,648,649,650,647,592,593,594,7,591,600,601,602,8,599,608,609,610,6,607,585,586,587,10,583,129,430,516,11,126,128,431,517,9,127,699,697,702,703,476,81,538,167,318,168,474,82,536,316,166,475,83,537,317,170,479,80,541,321,171,477,78,539,319,169,478,79,540,320,471,72,533,173,313,472,73,534,174,314,473,74,535,172,315,470,75,532,176,312,468,76,530,177,310,469,77,531,175,311,671,665,668,670,390,414,574,94,160,95,388,412,572,161,93,389,413,573,162,90,393,417,577,163,91,391,415,575,164,92,392,416,576,165,385,409,569,85,158,386,410,570,86,159,387,411,571,84,157,384,408,568,88,154,382,406,566,89,155,383,407,567,87,156,678,674,677,688 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#9741437d1171904ffa64043ea6d962aefa7dc37d5417f733d15a56c498f18cdb, 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 19:17:24 · history