Equation 677 Database

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Magma ff5ea5914f3b…

magma ff5ea5914f3b
Size
381
Isomorphism class hash
ff5ea5914f3b779e404080e4cfd70d942ec983abcaab03c9cf7421d883fb2da7
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 23:51:01
Display reorder
380,38,37,39,40,41,227,315,316,317,312,313,314,299,58,59,99,89,94,124,129,119,109,114,104,149,154,159,134,139,144,273,263,268,289,279,284,36,224,35,33,34,32,189,179,184,174,164,169,84,73,79,69,294,61,238,243,233,253,258,248,204,199,194,214,219,209,334,359,354,339,349,343,364,368,374,379,31,4,5,2,3,229,303,304,305,301,300,302,297,44,45,97,87,92,122,127,117,107,112,102,147,152,157,132,137,142,272,262,267,287,277,282,30,222,29,27,28,26,187,177,182,172,162,167,82,74,77,67,292,63,236,242,231,252,257,247,202,197,192,212,217,207,332,357,352,337,347,342,362,367,372,377,21,20,22,23,24,225,325,329,324,327,328,326,296,1,0,96,85,90,121,126,116,105,110,100,146,151,155,130,135,140,270,261,266,286,276,281,19,221,6,8,9,7,186,175,180,171,161,166,81,71,76,66,290,60,237,240,232,251,256,246,200,195,190,210,215,206,330,355,351,336,345,340,361,365,371,375,54,53,55,56,57,228,309,310,311,306,307,308,298,46,47,98,88,93,123,128,118,108,113,103,148,153,158,133,138,143,274,264,269,288,278,283,52,223,51,49,50,48,188,178,183,173,163,168,83,72,78,68,293,64,239,244,234,254,259,249,203,198,193,213,218,208,333,358,353,338,348,344,363,369,373,378,25,10,11,12,13,226,323,321,322,320,318,319,295,42,43,95,86,91,120,125,115,106,111,101,145,150,156,131,136,141,271,260,265,285,275,280,18,220,17,15,16,14,185,176,181,170,160,165,80,70,75,65,291,62,235,241,230,250,255,245,201,196,191,211,216,205,331,356,350,335,346,341,360,366,370,376 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {71} 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 23:51:02 · history