Equation 677 Database

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Magma 4d8d7df52797…

magma 4d8d7df52797
Size
381
Isomorphism class hash
4d8d7df52797a1afc65abf7fcabd622ddf215e431a87c83473a8fa5d7890b557
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:28:22
Display reorder
380,316,43,32,197,201,202,310,44,30,195,42,196,203,308,31,59,317,188,181,45,57,186,318,182,46,58,327,187,180,47,38,207,189,49,185,36,208,190,50,183,37,209,191,48,184,194,51,198,33,205,192,52,199,34,206,193,53,200,35,204,55,56,41,39,40,54,364,337,336,362,363,339,361,338,360,335,311,94,109,248,269,265,312,95,110,246,93,247,266,329,108,107,328,264,258,96,105,267,319,259,97,106,320,268,260,98,116,255,240,100,262,114,256,241,101,263,115,257,242,99,261,245,117,249,113,253,243,118,250,111,254,244,119,251,112,252,103,104,92,90,91,102,356,333,332,358,359,331,357,334,355,330,314,18,7,169,176,174,305,19,8,170,20,168,175,304,6,5,306,160,153,23,3,161,326,154,21,4,325,159,155,22,13,151,164,24,157,14,150,162,25,158,12,152,163,26,156,166,29,173,11,177,167,27,171,9,178,165,28,172,10,179,0,2,16,17,15,1,372,345,349,370,371,347,374,346,373,348,322,87,76,238,213,214,323,88,77,239,89,237,215,315,75,74,302,229,222,60,72,230,324,223,61,73,307,228,224,62,82,219,233,64,226,83,220,231,65,227,81,221,232,63,225,235,66,210,80,217,236,67,211,78,218,234,68,212,79,216,70,71,85,86,84,69,375,353,352,378,379,350,377,354,376,351,309,126,144,277,296,294,300,127,145,278,128,276,295,303,146,142,301,297,290,131,143,299,313,288,129,141,321,298,289,130,121,287,272,132,291,122,285,270,133,292,120,286,271,134,293,274,137,281,148,282,275,135,279,149,283,273,136,280,147,284,138,139,124,125,123,140,365,343,342,368,369,340,367,344,366,341 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#578df7f6f4684cb0945b9f1d69f2c004d864e77abb0574e906ded40734a79f14, 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 23:28:23 · history