Equation 677 Database

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Magma 7a92c83b7ef8…

magma 7a92c83b7ef8
Size
381
Isomorphism class hash
7a92c83b7ef88c17c63f9f91c2db5b055d7e9958ca2e24c548380d660e75aad7
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 23:42:06
Display reorder
380,160,251,70,210,81,1,121,261,170,306,141,230,308,51,220,90,10,131,270,181,145,236,309,55,225,96,16,136,275,186,241,150,310,60,201,101,21,110,280,191,41,46,26,31,36,165,256,307,75,215,85,290,126,265,176,311,155,246,65,205,106,5,116,285,196,296,375,346,365,330,360,336,351,356,341,371,161,250,71,211,80,0,120,260,171,305,140,231,300,50,221,91,11,130,271,180,146,235,302,56,226,95,15,135,276,185,240,151,303,61,200,100,20,111,281,190,40,45,25,30,35,166,255,301,76,216,86,291,125,266,175,304,156,245,66,206,105,6,115,286,195,295,379,345,366,331,362,335,350,355,340,372,162,252,72,212,82,2,122,262,172,323,142,232,319,52,222,92,12,132,272,182,147,237,320,57,227,97,17,137,277,187,242,152,321,62,202,102,22,112,282,192,42,47,27,32,37,167,257,318,77,217,87,292,127,267,177,322,157,247,67,207,107,7,117,287,197,297,376,347,369,332,361,337,352,357,342,374,163,253,73,213,83,3,123,263,173,328,143,233,324,53,223,93,13,133,273,183,148,238,325,58,228,98,18,138,278,188,243,153,326,63,203,103,23,113,283,193,43,48,28,33,38,168,258,329,78,218,88,293,128,268,178,327,158,248,68,208,108,8,118,288,198,298,377,348,367,333,363,338,353,358,343,373,164,254,74,214,84,4,124,264,174,317,144,234,313,54,224,94,14,134,274,184,149,239,314,59,229,99,19,139,279,189,244,154,315,64,204,104,24,114,284,194,44,49,29,34,39,169,259,312,79,219,89,294,129,269,179,316,159,249,69,209,109,9,119,289,199,299,378,349,368,334,364,339,354,359,344,370 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#bcdaeba3e5c42bac8c75df4a4ea039608cfd6919340934a2200e9da4b34d4d34, 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 23:42:07 · history