Equation 677 Database

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Magma b738d69a83e3…

magma b738d69a83e3
Size
381
Isomorphism class hash
b738d69a83e3336640be6db0654e2d36206a44cef9690adbde6b1842b6eae0e8
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 23:44:58
Display reorder
380,224,223,225,226,227,222,42,43,44,45,46,47,123,124,125,120,121,122,90,91,92,93,94,95,276,281,286,294,295,271,130,131,126,127,128,129,317,312,313,314,315,316,220,221,216,217,218,219,255,260,265,241,245,250,37,36,87,88,89,38,39,84,40,85,41,86,344,350,349,370,376,337,336,366,365,330,56,55,57,58,59,54,202,203,198,199,200,201,209,204,205,206,207,208,83,78,79,80,81,82,278,283,288,292,298,273,210,211,212,213,214,215,309,310,311,306,307,308,52,53,48,49,50,51,258,263,268,243,248,253,194,193,76,77,72,195,196,73,197,74,192,75,343,364,363,372,378,362,361,339,338,342,107,106,102,103,104,105,70,71,66,67,68,69,25,26,27,28,29,24,178,179,174,175,176,177,275,280,285,291,296,270,33,34,35,30,31,32,325,326,327,328,329,324,99,100,101,96,97,98,257,262,267,242,247,252,62,61,173,168,169,63,64,170,65,171,60,172,358,335,334,374,375,341,340,346,345,357,14,13,15,16,17,12,147,148,149,144,145,146,137,132,133,134,135,136,163,164,165,166,167,162,279,284,289,293,299,274,138,139,140,141,142,143,319,320,321,322,323,318,20,21,22,23,18,19,259,264,269,244,249,254,154,153,157,158,159,155,150,160,151,161,152,156,356,352,351,373,379,353,354,332,333,355,112,111,113,108,109,110,233,228,229,230,231,232,3,4,5,1,0,2,182,183,184,185,180,181,277,282,287,290,297,272,10,11,6,7,8,9,303,304,305,301,300,302,119,114,115,116,117,118,256,261,266,240,246,251,234,239,188,189,190,235,236,191,237,186,238,187,359,331,369,371,377,367,368,347,348,360 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {74} 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 23:44:58 · history