Equation 677 Database

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Magma ad8121149e06…

magma ad8121149e06
Size
595
Isomorphism class hash
ad8121149e06b907e6c26392431d72fda68ddee3a7f9741422d701e29fb7f71e
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 18:51:13
Display reorder
315,314,316,317,312,313,319,318,320,321,322,323,504,505,506,507,508,509,461,466,462,463,464,465,273,275,274,272,271,270,555,581,588,587,594,495,497,492,493,494,496,380,379,381,378,473,382,402,401,403,404,405,406,376,375,377,372,373,374,346,345,347,342,343,344,396,395,397,398,399,400,340,339,341,336,337,338,179,178,177,175,176,174,15,17,16,13,14,12,10,9,11,8,6,7,18,20,19,22,23,21,26,25,24,27,28,29,113,112,111,108,109,110,217,216,218,219,220,221,117,119,118,114,115,116,168,170,169,171,172,173,550,541,521,517,510,525,530,545,535,576,589,566,556,572,583,562,483,485,480,481,482,484,414,413,415,416,417,418,422,421,423,424,419,420,407,412,408,409,410,411,284,283,285,286,287,282,430,429,425,426,427,428,281,280,277,276,278,279,231,233,232,230,228,229,84,86,85,88,89,87,79,78,80,83,81,82,93,95,94,91,92,90,75,77,76,73,74,72,5,4,3,1,0,2,234,236,235,239,237,238,268,267,269,265,266,264,223,222,224,226,227,225,552,542,524,519,514,529,534,549,537,579,593,570,557,575,586,565,502,503,499,500,501,498,387,386,388,383,384,385,467,472,468,469,470,471,391,390,392,393,394,389,306,311,307,308,309,310,297,296,298,299,294,295,301,300,302,303,304,305,214,213,215,210,211,212,159,161,160,157,158,156,153,155,154,151,152,150,162,164,163,166,167,165,146,145,144,147,148,149,62,61,60,63,64,65,56,55,54,58,59,57,66,68,67,69,70,71,206,205,204,209,207,208,553,540,523,518,513,528,533,548,538,578,592,569,560,574,585,564,474,477,478,479,475,476,334,333,335,330,331,332,446,445,447,448,443,444,327,326,328,329,324,325,369,368,370,371,366,367,290,289,291,292,293,288,364,363,365,360,361,362,106,105,107,102,103,104,190,189,191,188,186,187,184,183,185,182,180,181,193,192,194,197,195,196,198,200,199,202,203,201,140,139,138,141,142,143,252,254,253,257,255,256,135,137,136,132,133,134,98,97,96,101,99,100,554,543,520,515,511,526,531,546,539,577,590,567,558,571,582,561,487,489,490,491,486,488,359,358,354,355,356,357,453,452,454,449,450,451,352,351,353,348,349,350,438,437,439,440,441,442,455,460,456,457,458,459,433,432,434,435,436,431,125,124,123,121,122,120,48,50,49,52,53,51,42,44,43,46,47,45,35,34,33,30,31,32,41,40,39,36,37,38,244,243,245,242,240,241,263,262,261,259,260,258,251,250,249,248,246,247,129,131,130,126,127,128,551,544,522,516,512,527,532,547,536,580,591,568,559,573,584,563 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#e4013d0178842fa1abe6ac84eb6d8732370ca50237187a2a953024cf339ab2c2, M = the submagma generated by {12, 30} (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 18:51:14 · history