Equation 677 Database

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Magma cd9ae33e321d…

magma cd9ae33e321d
Size
381
Isomorphism class hash
cd9ae33e321d5f70a9f361cb51ae7db6403e4e8987416877517c57cc233aed64
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 23:44:50
Display reorder
380,283,244,131,161,191,221,314,315,316,317,312,313,279,127,157,188,217,262,106,107,102,103,104,105,253,278,126,156,186,216,61,62,63,64,65,60,66,67,68,69,70,71,254,282,130,160,190,220,159,189,219,243,281,129,100,99,284,132,162,101,96,192,97,222,98,255,335,334,368,349,347,374,348,365,350,360,286,256,134,164,194,223,306,307,308,309,310,311,280,128,158,187,218,263,44,45,46,47,42,43,240,271,121,150,182,212,34,35,30,31,32,33,25,26,27,28,29,24,261,276,125,155,185,215,177,207,237,267,277,147,38,37,285,133,163,39,40,193,41,224,36,245,352,341,366,330,339,361,346,373,351,379,295,248,142,172,202,232,328,329,324,325,326,327,297,144,174,204,234,259,78,79,80,81,82,83,249,296,143,173,203,233,115,116,117,118,119,114,112,113,108,109,110,111,250,298,145,175,205,235,176,206,236,251,299,146,72,77,294,141,171,73,74,201,75,231,76,266,357,333,378,338,358,377,359,371,331,362,293,269,149,179,209,239,323,318,319,320,321,322,287,135,165,195,225,264,16,17,12,13,14,15,242,275,124,154,184,214,59,54,55,56,57,58,50,51,52,53,48,49,257,290,138,168,198,228,169,199,229,247,291,139,18,23,292,140,170,19,20,200,21,230,22,258,356,337,375,332,345,364,355,372,336,363,272,241,122,152,181,211,301,300,302,303,304,305,274,123,153,183,213,252,89,84,85,86,87,88,268,273,148,178,208,238,8,9,10,11,6,7,5,1,0,2,3,4,246,289,137,167,197,227,166,196,226,265,288,136,91,90,270,120,151,92,93,180,94,210,95,260,340,344,367,354,343,369,353,376,342,370 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 = {72} 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 23:44:51 · history