Equation 677 Database

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Magma 6c8e45ea2640…

magma 6c8e45ea2640
Size
381
Isomorphism class hash
6c8e45ea26409707e5e454018ae2e645e6ed734e2588c0e3c32e1fab6fcdada6
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 23:41:54
Display reorder
380,229,225,207,216,233,220,237,211,325,215,226,230,208,217,231,221,213,238,212,326,214,228,227,209,218,232,219,239,210,323,203,324,181,190,204,194,186,234,185,199,201,327,200,182,191,205,192,187,235,183,322,202,198,180,189,206,193,188,236,184,197,195,222,223,224,196,349,351,338,378,374,366,350,339,331,332,292,285,259,268,299,275,255,263,309,264,286,293,260,269,297,274,265,256,261,329,266,291,287,258,267,298,273,257,262,308,289,307,245,254,294,271,250,241,246,284,290,306,282,243,252,295,272,251,242,247,328,288,283,244,253,296,270,249,240,248,278,276,279,280,281,277,352,368,361,376,341,340,354,375,367,353,9,8,18,27,13,1,17,22,300,26,6,10,19,28,14,0,24,15,23,302,25,11,7,20,29,12,2,16,21,301,38,304,47,56,39,57,52,43,48,34,36,305,35,45,54,40,58,53,44,49,303,37,33,46,55,41,59,51,42,50,32,30,5,3,4,31,363,370,371,369,333,334,362,342,355,356,127,123,136,145,131,175,132,140,321,141,124,128,137,146,129,176,142,133,138,319,143,126,125,135,144,130,174,134,139,320,153,318,162,171,157,178,170,161,166,152,154,316,150,163,172,158,179,168,159,167,317,155,151,164,173,156,177,169,160,165,147,148,120,121,122,149,347,348,373,377,345,346,330,365,372,337,98,94,107,116,99,117,103,108,311,112,95,96,105,114,100,118,113,104,109,312,111,97,93,106,115,101,119,102,110,310,69,314,78,87,73,60,86,77,82,68,70,315,66,79,88,74,61,84,75,83,313,71,67,80,89,72,62,85,76,81,63,64,91,92,90,65,336,357,335,379,360,364,344,358,343,359 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#b69d7fba7733d8ec194d1fe470c23299a6bbf7f834fcda60a95bfadcfba0958c, 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 23:41:55 · history