Equation 677 Database

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Magma ccb9333cbaa7…

magma ccb9333cbaa7
Size
381
Isomorphism class hash
ccb9333cbaa7d4dd3f1fc665bb1a3c4874c433f61e65d43ec538f10c86d22d34
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 23:44:29
Display reorder
380,222,227,223,224,225,226,188,189,190,191,186,187,306,307,308,309,310,311,144,145,146,147,148,149,155,150,151,152,153,154,220,221,216,217,218,219,83,78,79,80,81,82,185,180,181,182,183,184,75,76,77,72,73,74,250,240,241,251,261,260,270,271,280,281,290,291,370,367,343,354,379,360,361,342,366,355,124,123,125,120,121,122,213,214,215,210,211,212,300,302,303,304,305,301,85,86,87,88,89,84,90,91,92,93,94,95,130,131,126,127,128,129,166,167,162,163,164,165,204,205,206,207,208,209,158,159,160,161,156,157,255,246,247,256,267,266,276,277,286,287,296,297,376,350,357,344,377,364,365,356,351,345,60,65,61,62,63,64,0,2,3,4,5,1,328,329,324,325,326,327,41,36,37,38,39,40,46,47,42,43,44,45,66,67,68,69,70,71,49,50,51,52,53,48,6,7,8,9,10,11,55,56,57,58,59,54,258,249,248,257,268,269,279,278,289,288,299,298,378,338,336,332,371,334,335,337,339,333,197,196,192,193,194,195,237,238,239,234,235,236,319,320,321,322,323,318,108,109,110,111,112,113,119,114,115,116,117,118,203,198,199,200,201,202,33,34,35,30,31,32,228,229,230,231,232,233,25,26,27,28,29,24,252,242,243,253,263,262,272,273,282,283,292,293,372,362,331,349,373,368,369,330,363,348,175,174,176,177,178,179,142,143,138,139,140,141,315,316,317,312,313,314,106,107,102,103,104,105,97,98,99,100,101,96,173,168,169,170,171,172,18,19,20,21,22,23,133,134,135,136,137,132,16,17,12,13,14,15,254,245,244,259,264,265,275,274,285,284,295,294,375,359,340,347,374,352,353,341,358,346 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 = {67} 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 23:44:30 · history