Equation 677 Database

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Magma c75fe8b63a6d…

magma c75fe8b63a6d
Size
381
Isomorphism class hash
c75fe8b63a6d7e021063bbcf59e07e77a431553ff3149bacd7f47e2b68cb6cda
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 23:21:32
Display reorder
380,97,72,9,318,162,276,185,250,137,226,320,157,286,2,195,107,245,67,132,221,171,237,261,122,147,321,15,82,57,211,175,241,266,112,152,322,20,87,62,201,47,37,42,32,26,102,77,127,167,319,291,281,190,256,215,180,230,270,117,142,323,10,92,52,206,296,357,335,330,352,367,340,377,362,347,372,96,71,7,304,160,275,187,251,135,225,303,155,285,1,197,106,246,66,130,220,172,236,260,121,146,300,16,81,55,210,176,240,265,110,151,302,21,85,60,200,46,36,41,30,25,101,75,126,165,305,290,280,191,255,216,182,232,271,115,141,301,11,90,50,205,295,355,336,331,351,365,341,375,361,345,371,99,74,5,316,164,277,189,253,139,228,315,159,288,0,199,109,248,69,134,224,174,239,263,124,149,313,17,84,59,214,179,243,268,114,154,314,22,89,64,204,49,39,44,34,29,104,79,129,169,317,292,283,194,258,219,184,234,273,119,144,312,12,94,54,209,299,359,337,332,354,369,343,379,364,349,374,98,73,6,324,163,278,188,252,138,229,326,158,287,3,198,108,247,68,133,223,173,238,262,123,148,327,18,83,58,213,178,242,267,113,153,328,23,88,63,203,48,38,43,33,28,103,78,128,168,325,293,282,193,257,218,183,233,272,118,143,329,13,93,53,208,298,358,338,333,353,368,342,378,363,348,373,95,70,8,310,161,279,186,254,136,227,309,156,289,4,196,105,249,65,131,222,170,235,264,120,145,307,19,80,56,212,177,244,269,111,150,308,24,86,61,202,45,35,40,31,27,100,76,125,166,311,294,284,192,259,217,181,231,274,116,140,306,14,91,51,207,297,356,339,334,350,366,344,376,360,346,370 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#432e4c006dcd7a87bd51f20718c8a2600c80c9e6f4728c9b2189310a93934f23, 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 23:21:33 · history