Equation 677 Database

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Magma e6ae279b0f2c…

magma e6ae279b0f2c
Size
381
Isomorphism class hash
e6ae279b0f2c128ac90561b1b7a1873c0e4db6145baf57bad48e2c521636f83d
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 23:35:05
Display reorder
380,267,314,252,276,245,284,275,246,291,299,268,317,253,294,277,241,285,270,250,292,269,306,254,295,278,240,286,271,248,293,264,309,255,296,279,242,287,272,249,288,265,310,256,297,280,243,282,273,251,289,266,312,298,257,281,244,283,274,247,290,259,261,262,263,258,260,350,348,367,352,351,368,379,378,349,366,101,322,88,108,75,115,102,82,62,69,96,324,89,70,109,76,116,103,83,63,97,326,84,71,110,77,117,104,78,64,98,328,85,66,111,72,118,105,79,65,99,319,86,67,112,73,119,106,80,60,100,320,68,87,113,74,114,107,81,61,94,90,91,92,93,95,358,356,334,336,359,335,338,337,357,376,17,315,4,24,50,31,18,57,37,44,12,316,5,45,25,51,32,19,58,38,13,307,1,46,26,52,33,20,59,39,14,308,0,47,27,53,34,21,54,40,15,311,2,42,28,48,35,22,55,41,16,313,43,3,29,49,30,23,56,36,10,6,7,8,9,11,354,375,369,333,353,370,355,332,331,330,219,301,206,238,193,231,226,200,180,187,220,300,207,188,239,194,228,227,201,181,221,302,208,189,234,195,232,222,202,182,216,303,209,190,235,196,233,223,203,183,217,304,204,191,236,197,229,224,198,184,218,305,186,205,237,192,230,225,199,185,212,214,215,210,211,213,374,346,345,363,377,373,362,364,347,365,145,329,132,158,125,165,152,126,171,178,146,318,133,179,159,120,166,153,127,172,147,321,134,174,160,121,167,154,128,173,148,323,135,175,161,122,162,155,129,168,149,325,136,176,156,123,163,150,130,169,144,327,177,137,157,124,164,151,131,170,138,140,141,142,143,139,360,371,342,372,361,343,341,344,340,339 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#890afe7d18fc5829c22763230887bcc55424b15f1aafa8ec136cb8772e59bad6, 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 23:35:06 · history