Equation 677 Database

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Magma 53c8a1c5e39d…

magma 53c8a1c5e39d
Size
381
Isomorphism class hash
53c8a1c5e39de4117c95cf6aa8dadaec6354bf08aac1848e4247688147b62f28
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 23:26:07
Display reorder
380,258,253,263,268,243,248,293,298,273,278,283,288,120,121,122,123,124,125,137,132,133,134,135,136,198,203,208,183,188,193,129,130,131,126,127,128,142,143,138,139,140,141,145,146,147,148,149,144,213,218,223,227,233,238,173,178,153,158,163,168,308,310,306,309,311,307,367,353,358,350,354,352,351,372,364,377,255,250,260,266,240,245,290,295,270,275,280,285,8,9,10,11,6,7,22,23,18,19,20,21,196,201,205,181,186,191,29,24,25,26,27,28,3,4,5,1,0,2,17,12,13,14,15,16,210,215,222,226,231,236,171,176,150,155,160,166,324,326,328,325,327,329,366,341,356,332,342,340,344,371,362,376,256,251,261,265,241,246,291,296,271,276,281,286,36,37,38,39,40,41,50,51,52,53,48,49,195,200,206,180,185,190,54,55,56,57,58,59,35,30,31,32,33,34,46,47,42,43,44,45,211,216,221,225,230,235,170,175,151,156,161,165,320,322,318,321,323,319,368,337,355,331,345,343,346,373,361,378,257,252,262,267,242,247,292,297,272,277,282,287,98,99,100,101,96,97,112,113,108,109,110,111,197,202,207,182,187,192,119,114,115,116,117,118,93,94,95,90,91,92,107,102,103,104,105,106,212,217,220,228,232,237,172,177,152,157,162,167,313,315,317,314,316,312,369,336,357,338,333,334,349,374,363,379,259,254,264,269,244,249,294,299,274,279,284,289,61,62,63,64,65,60,75,76,77,72,73,74,199,204,209,184,189,194,80,81,82,83,78,79,85,86,87,88,89,84,69,70,71,66,67,68,214,219,224,229,234,239,174,179,154,159,164,169,302,304,301,303,305,300,365,335,359,339,347,330,348,370,360,375 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:26:07 · history