Equation 677 Database

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Magma 2ad903124ed9…

magma 2ad903124ed9
Size
381
Isomorphism class hash
2ad903124ed9cabe9a3edb3cc4461f4179f56ebc2be42c982c2b137c388c37a0
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 23:45:59
Display reorder
380,289,239,39,89,139,189,44,94,144,199,244,294,214,264,14,64,114,164,211,261,11,61,111,161,110,160,210,260,10,60,279,29,79,129,179,229,99,149,194,249,299,49,234,284,34,84,134,184,314,315,316,317,312,313,263,13,63,113,163,213,12,212,62,112,162,262,342,364,366,375,350,358,346,352,351,372,287,237,37,87,137,187,42,92,142,197,242,292,220,270,20,70,120,170,222,272,22,72,122,172,121,171,221,271,21,71,277,27,77,127,177,227,97,147,192,247,297,47,232,282,32,82,132,182,307,308,309,310,311,306,274,24,74,124,174,224,23,223,73,123,173,273,356,362,367,377,357,331,343,340,330,373,288,238,38,88,138,188,43,93,143,198,243,293,207,257,7,57,107,157,209,259,9,59,109,159,108,158,208,258,8,58,278,28,78,128,178,228,98,148,193,248,298,48,233,283,33,83,133,183,321,322,323,318,319,320,256,6,56,106,156,206,5,205,55,105,155,255,344,360,368,376,341,336,347,332,359,371,286,236,36,86,136,186,40,90,140,195,240,290,200,250,1,51,101,151,203,253,3,53,103,153,102,152,202,252,2,52,276,25,75,125,176,226,96,145,190,246,296,46,230,280,30,80,130,180,326,327,328,329,324,325,251,0,50,100,150,201,4,204,54,104,154,254,345,361,369,379,355,337,339,338,334,370,285,235,35,85,135,185,41,91,141,196,241,291,216,266,16,66,116,166,218,268,18,68,118,168,117,167,217,267,17,67,275,26,76,126,175,225,95,146,191,245,295,45,231,281,31,81,131,181,302,303,304,305,301,300,265,15,65,115,165,215,19,219,69,119,169,269,354,363,365,378,335,349,353,333,348,374 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 = {76} 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 23:46:00 · history