Equation 677 Database

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Magma c37d9309ddb4…

magma c37d9309ddb4
Size
595
Isomorphism class hash
c37d9309ddb4ccdda5efbbc53ec60dda14e896655d54f318e42ec696e19b6241
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 13:09:43
Display reorder
120,125,121,122,123,124,10,15,11,12,13,14,76,75,77,78,79,74,23,22,24,19,20,21,482,480,481,483,484,485,526,578,562,563,574,247,248,180,250,251,249,167,127,128,129,130,126,89,88,84,85,86,87,17,16,18,191,192,160,199,201,200,162,66,67,148,147,149,146,150,241,176,242,238,239,240,177,196,195,197,161,193,194,365,364,363,362,360,361,293,292,291,290,288,289,498,497,499,501,502,500,372,374,373,376,377,375,437,436,435,434,432,433,488,487,486,490,491,489,331,330,332,333,334,335,356,355,354,357,358,359,548,547,539,515,538,524,533,532,553,560,593,591,576,554,575,579,109,111,110,113,108,112,107,106,102,103,104,105,33,32,34,35,36,31,39,38,40,41,42,37,100,99,101,96,97,98,49,53,50,51,52,198,210,166,211,208,209,165,233,237,175,234,235,236,504,495,496,493,494,492,431,430,429,428,426,427,478,477,479,474,476,475,444,446,445,448,449,447,509,507,506,508,505,503,469,470,471,472,473,468,320,319,318,322,323,321,387,389,388,385,386,384,523,522,514,550,549,528,529,527,566,567,568,556,586,590,572,571,58,54,59,56,57,55,136,135,131,132,133,134,114,119,115,116,117,118,27,26,28,29,30,25,92,91,93,94,95,90,152,151,153,154,155,263,256,253,257,258,259,232,255,254,252,260,261,262,268,267,269,264,266,265,380,379,378,383,381,382,405,407,406,402,403,404,298,297,299,296,294,295,396,398,397,399,400,401,285,287,286,284,282,283,464,465,463,462,466,467,395,394,393,390,391,392,535,531,518,520,519,511,521,510,559,565,557,594,570,585,589,580,47,43,48,45,46,44,144,222,219,220,172,221,205,163,206,164,207,204,182,181,156,1,2,0,80,83,81,82,202,203,179,243,245,246,178,244,171,216,217,218,215,170,226,225,227,173,223,224,341,340,339,338,336,337,276,278,277,279,280,281,327,329,328,324,325,326,416,415,414,417,418,419,438,440,439,441,442,443,300,302,301,305,303,304,410,409,408,412,413,411,456,460,459,457,458,461,544,546,517,512,513,525,534,516,551,564,555,592,577,587,582,584,72,68,73,70,71,69,145,230,231,174,228,229,185,157,186,187,158,188,190,189,159,7,8,9,4,3,5,6,184,183,214,213,168,212,169,137,139,138,140,141,142,143,60,65,61,62,63,64,425,424,423,422,420,421,450,452,451,453,454,455,371,370,369,368,366,367,317,316,315,312,313,314,307,306,308,310,311,309,342,344,343,347,345,346,273,275,274,272,270,271,352,351,353,350,348,349,541,540,536,545,543,530,542,537,552,569,561,581,573,558,583,588 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = the submagma generated by {6, 18} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 13:09:44 · history