Equation 677 Database

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Magma a1aadfeecc3d…

magma a1aadfeecc3d
Size
381
Isomorphism class hash
a1aadfeecc3d0051c0b65b2fcdde4a1827d82ed596deb90369eb664f5b93718e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:31:20
Display reorder
380,224,199,80,90,130,107,170,184,274,264,145,159,254,244,249,229,234,55,70,60,18,9,311,306,49,39,34,214,204,209,86,76,104,95,120,125,116,111,176,165,189,194,284,279,269,259,137,141,154,164,239,50,66,219,289,24,14,4,309,307,310,308,44,294,29,295,379,359,364,349,334,339,354,344,368,374,223,198,84,94,134,109,174,183,273,263,149,158,253,243,248,228,233,59,74,64,17,8,305,301,48,38,33,213,203,208,89,79,103,99,124,129,119,114,179,169,188,193,283,278,268,258,139,144,153,163,238,54,69,218,288,23,13,3,303,300,304,302,43,293,28,299,378,358,363,348,333,338,353,343,367,373,221,197,83,91,131,108,172,182,271,261,148,156,252,242,246,227,231,57,72,63,15,5,322,320,45,36,31,211,201,207,88,77,101,97,122,126,118,112,178,168,186,192,281,276,265,256,138,142,151,161,237,52,67,217,285,20,10,0,323,318,321,319,40,290,27,296,375,356,361,346,332,335,351,341,366,371,220,195,81,93,133,105,171,180,270,262,146,157,250,240,245,226,230,58,71,61,16,7,324,328,46,35,30,210,200,205,85,75,102,98,123,128,115,110,175,167,185,190,280,275,267,257,136,140,152,162,235,53,65,215,286,22,11,1,325,329,326,327,41,291,26,298,377,357,362,347,330,337,352,342,369,372,222,196,82,92,132,106,173,181,272,260,147,155,251,241,247,225,232,56,73,62,19,6,315,313,47,37,32,212,202,206,87,78,100,96,121,127,117,113,177,166,187,191,282,277,266,255,135,143,150,160,236,51,68,216,287,21,12,2,316,314,317,312,42,292,25,297,376,355,360,345,331,336,350,340,365,370 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {73} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:31:21 · history