Equation 677 Database

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Magma fa940874b611…

magma fa940874b611
Size
381
Isomorphism class hash
fa940874b61196384dce0ab49c5d86d35401ba28c6fe819fa270d0b5cf502e44
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 23:46:19
Display reorder
380,137,147,277,287,297,142,312,313,314,315,316,317,57,58,59,60,61,62,197,202,207,182,187,192,232,237,212,217,222,227,257,262,267,242,247,252,73,74,69,70,71,72,64,65,66,67,68,63,172,177,152,157,162,167,80,75,76,77,78,79,272,55,282,292,54,56,353,343,369,362,331,336,347,358,372,379,136,146,276,286,296,141,327,328,329,324,325,326,107,102,103,104,105,106,195,200,205,181,186,191,230,236,211,216,220,225,256,260,265,241,246,251,89,90,91,92,87,88,86,81,82,83,84,85,170,175,151,156,161,165,96,97,98,93,94,95,273,99,283,293,101,100,351,344,367,363,338,334,346,357,373,377,135,145,275,285,295,140,305,301,300,302,303,304,3,4,5,6,7,8,196,201,206,180,185,190,231,235,210,215,221,226,255,261,266,240,245,250,19,20,15,16,17,18,10,11,12,13,14,9,171,176,150,155,160,166,26,21,22,23,24,25,271,0,281,291,2,1,352,341,366,360,332,333,345,356,371,376,138,148,278,288,298,143,310,311,306,307,308,309,111,112,113,114,115,116,198,203,208,183,188,193,233,238,213,218,223,228,258,263,268,243,248,253,127,128,123,124,125,126,118,119,120,121,122,117,173,178,153,158,163,168,134,129,130,131,132,133,274,109,284,294,108,110,354,342,368,364,330,339,348,359,374,378,139,149,279,289,299,144,321,322,323,318,319,320,32,27,28,29,30,31,199,204,209,184,189,194,234,239,214,219,224,229,259,264,269,244,249,254,44,39,40,41,42,43,35,36,37,38,33,34,174,179,154,159,164,169,45,46,47,48,49,50,270,52,280,290,51,53,350,340,365,361,335,337,349,355,370,375 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {71} 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 23:46:19 · history