Equation 677 Database

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Magma 80bfcb0d5da3…

magma 80bfcb0d5da3
Size
705
Isomorphism class hash
80bfcb0d5da37e041167e40f2ec18c2e18685f14405ae0ae94195f93cb51bd3a
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 18:25:01
Display reorder
660,110,443,385,353,329,111,330,444,386,354,442,328,112,384,352,332,109,446,388,356,333,107,447,389,357,331,108,445,387,355,116,335,449,391,359,336,450,392,117,360,334,448,390,118,358,452,338,394,115,362,453,339,395,113,363,451,337,393,114,361,677,676,681,674,15,455,238,178,146,16,147,456,239,176,454,148,17,240,177,145,14,458,241,174,143,12,459,242,175,144,13,457,243,173,21,152,461,236,169,153,462,237,22,167,154,460,235,23,168,464,151,232,20,172,465,149,233,18,170,463,150,234,19,171,671,672,662,661,104,249,46,397,575,105,576,247,47,398,248,574,106,45,396,578,103,245,42,400,579,101,246,43,401,577,102,244,44,399,95,581,255,37,403,582,253,38,96,404,580,254,36,97,402,251,584,40,98,406,252,585,41,99,407,250,583,39,100,405,682,678,686,684,208,365,217,636,375,206,376,366,215,634,364,374,207,216,635,378,204,368,220,639,379,205,369,218,637,377,203,367,219,638,214,381,371,223,642,382,372,221,212,640,380,370,222,213,641,646,647,644,210,648,656,657,654,211,659,373,383,224,209,643,700,702,697,699,5,515,200,479,587,3,588,516,201,480,514,586,4,202,478,590,0,518,199,482,591,2,519,197,483,589,1,517,198,481,11,593,521,191,485,594,522,192,9,486,592,520,193,10,484,524,596,194,7,488,525,597,195,8,489,523,595,196,6,487,689,692,693,696,78,551,292,503,309,79,307,552,293,504,550,308,77,294,502,305,81,554,295,506,306,82,555,296,507,304,80,553,297,505,76,315,557,298,509,313,558,299,74,510,314,556,300,75,508,560,311,301,72,512,561,312,302,73,513,559,310,303,71,511,669,665,667,668,275,84,467,563,122,276,123,85,468,564,83,124,274,466,562,121,278,87,470,566,119,279,88,471,567,120,277,86,469,565,273,128,90,473,569,129,91,474,271,570,130,89,472,272,568,93,127,476,269,572,94,125,477,270,573,92,126,475,268,571,691,695,690,694,257,611,284,409,341,258,342,612,285,410,610,340,256,283,408,344,260,614,280,412,345,261,615,281,413,343,259,613,282,411,263,347,617,290,415,348,618,291,264,416,346,616,289,262,414,620,350,286,266,418,621,351,287,267,419,619,349,288,265,417,673,679,687,675,135,61,56,229,421,136,422,62,54,230,63,420,134,55,231,424,131,64,52,228,425,132,65,53,226,423,133,66,51,227,141,427,67,60,48,428,68,58,142,49,426,69,59,140,50,650,651,649,137,645,653,658,652,138,655,70,429,57,139,225,703,704,698,701,186,491,539,162,31,187,32,492,540,163,490,30,185,538,161,34,189,494,542,165,35,190,495,543,166,33,188,493,541,164,184,29,497,545,160,27,498,546,182,158,28,496,544,183,159,500,25,548,180,156,501,26,549,181,157,499,24,547,179,155,666,663,664,670,317,431,527,599,623,318,624,432,528,600,430,622,316,526,598,626,320,434,530,602,627,321,435,531,603,625,319,433,529,601,323,629,437,533,605,630,438,534,324,606,628,436,532,322,604,440,632,536,326,608,441,633,537,327,609,439,631,535,325,607,683,685,680,688 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#82fe73547f12a148ba897be501ddca2fd72765d56930c9a3792aacda34cfdc1d, 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 18:25:02 · history