Equation 677 Database

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Magma 4f9e08a87c84…

magma 4f9e08a87c84
Size
381
Isomorphism class hash
4f9e08a87c84feb85ea446e90c6591d6c7a61d64883e0044192b7c712f063650
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:27:10
Display reorder
380,99,145,274,114,277,278,100,146,275,115,279,101,147,270,116,96,280,148,271,117,97,281,149,272,118,144,276,98,273,119,79,189,239,325,121,190,80,234,323,122,191,81,235,324,123,82,186,236,329,124,83,187,237,322,125,78,188,238,326,120,257,253,254,255,256,252,363,332,339,364,342,334,366,333,365,367,102,15,286,130,244,245,103,16,287,131,240,104,17,282,126,105,241,12,283,127,106,242,13,284,128,14,243,107,285,129,133,163,289,301,88,164,134,290,300,89,165,135,291,315,84,136,166,292,302,85,137,167,293,303,86,132,162,288,304,87,260,262,263,258,259,261,376,337,345,377,346,350,374,349,373,375,63,40,251,91,206,207,64,41,246,92,208,65,36,247,93,60,209,37,248,94,61,204,38,249,95,39,205,62,250,90,111,194,265,309,50,195,112,266,305,51,196,113,267,327,52,108,197,268,306,53,109,192,269,307,48,110,193,264,308,49,221,217,218,219,220,216,356,340,341,360,331,338,362,330,361,358,34,58,232,76,296,297,35,59,233,77,298,30,54,228,72,31,299,55,229,73,32,294,56,230,74,57,295,33,231,75,44,212,200,312,140,213,45,201,313,141,214,46,202,314,142,47,215,203,328,143,42,210,198,310,138,43,211,199,311,139,184,180,181,182,183,185,370,344,348,371,336,343,368,335,372,369,4,27,157,7,223,224,5,28,158,8,225,1,29,159,9,0,226,24,160,10,2,227,25,161,11,26,222,3,156,6,21,179,171,321,67,174,22,172,316,68,175,23,173,317,69,18,176,168,318,70,19,177,169,319,71,20,178,170,320,66,151,152,153,154,155,150,379,354,347,355,351,352,359,353,357,378 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#522c4255bab6feaf8dded3275865d4dfd6bf32ecc3cda598bb7d756acc9d9472, 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 23:27:11 · history