Equation 677 Database

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Magma 536972a3d0c5…

magma 536972a3d0c5
Size
381
Isomorphism class hash
536972a3d0c5df4fa9872c76bf951d1f0fc79e56b1b7e208768ae784e5926374
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 23:40:00
Display reorder
380,306,249,265,281,256,296,258,289,282,272,250,307,266,276,257,297,259,290,283,273,308,251,267,277,252,298,260,291,284,274,309,247,268,254,299,261,292,285,275,278,246,315,269,279,253,294,262,293,286,270,248,305,264,280,255,295,263,288,287,271,242,244,245,241,240,243,338,354,355,356,376,352,337,351,372,353,325,36,54,6,42,24,48,18,12,1,37,327,55,7,43,25,49,19,13,0,329,38,56,8,44,26,50,20,14,2,318,39,57,45,27,51,21,15,3,9,40,321,58,10,46,28,52,22,16,4,41,323,59,11,47,29,53,23,17,5,34,30,31,32,33,35,367,336,371,347,349,335,350,348,375,370,313,202,220,230,207,189,212,184,238,225,203,314,221,231,208,190,213,185,239,226,311,198,216,232,209,191,214,180,234,227,312,199,217,204,186,215,181,235,222,233,200,310,218,228,205,187,210,182,236,223,201,317,219,229,206,188,211,183,237,224,192,194,195,196,197,193,368,333,346,332,334,366,369,330,331,374,328,171,130,140,176,158,122,153,148,135,172,319,131,141,177,159,123,154,149,136,320,173,126,142,178,160,124,155,144,137,322,168,127,179,161,125,150,145,132,143,169,324,128,138,174,156,120,151,146,133,170,326,129,139,175,157,121,152,147,134,164,166,167,162,163,165,357,360,373,339,377,359,378,358,340,341,300,66,84,96,72,114,78,108,102,90,67,302,85,97,73,115,79,109,103,91,303,68,86,98,74,116,80,110,104,92,304,69,87,75,117,81,111,105,93,99,70,301,88,100,76,118,82,112,106,94,71,316,89,101,77,119,83,113,107,95,64,60,61,62,63,65,361,364,379,342,345,344,365,362,343,363 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#a8bf484a26d6d970fa38b68ff8761a583a974592ed3d92ce3524bc40b356dd63, 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 23:40:01 · history