Equation 677 Database

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Magma 6c28a1512ea8…

magma 6c28a1512ea8
Size
381
Isomorphism class hash
6c28a1512ea8f928bf8d3ebf4553d5b2354ced1eec58d6451a93882f3f8a1a5d
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 23:32:36
Display reorder
380,314,60,97,78,103,110,115,92,84,74,116,93,317,61,98,79,104,111,85,75,310,62,99,80,105,112,86,76,117,94,311,63,100,81,106,113,118,95,87,77,312,64,101,82,107,108,119,90,88,72,313,65,96,83,102,109,114,91,89,73,66,68,69,70,71,67,364,366,344,367,368,379,378,343,376,365,321,34,7,52,13,20,25,2,58,42,26,3,323,35,8,53,14,21,59,43,325,30,9,48,15,22,54,44,27,4,327,31,10,49,16,23,28,5,55,45,329,32,11,50,17,18,29,1,56,46,318,33,6,51,12,19,24,0,57,47,40,36,37,38,39,41,346,332,345,369,331,330,350,349,348,347,308,214,187,232,193,200,205,182,238,222,206,183,309,215,188,233,194,201,239,223,304,210,189,228,195,202,234,224,207,184,305,211,190,229,196,203,208,185,235,225,306,212,191,230,197,198,209,180,236,226,307,213,186,231,192,199,204,181,237,227,220,216,217,218,219,221,373,374,363,375,372,339,342,341,340,362,300,264,240,285,246,254,260,295,292,280,261,296,302,265,244,286,247,255,293,281,303,266,242,287,248,256,288,276,262,297,301,267,243,282,249,257,263,298,289,277,315,268,245,283,250,252,258,299,290,278,316,269,241,284,251,253,259,294,291,279,271,273,274,275,270,272,361,359,338,377,371,360,356,355,358,357,322,167,140,121,146,153,158,135,127,175,159,136,324,162,141,122,147,154,128,176,326,163,142,123,148,155,129,177,160,137,328,164,143,124,149,150,161,132,130,178,319,165,138,125,144,151,156,133,131,179,320,166,139,120,145,152,157,134,126,174,173,169,170,171,172,168,370,352,353,336,354,337,335,334,333,351 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#7ff2d65e3937a66fa34cc89b98c8a93554d71488124527b95614f86b1a7e6912, M = {66} 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 23:32:37 · history