Equation 677 Database

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Magma 75ee5ef0ae30…

magma 75ee5ef0ae30
Size
381
Isomorphism class hash
75ee5ef0ae3062b07ee9e82fb452600d7df105239b68f999f3613fa9d3e73bcf
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 23:27:19
Display reorder
380,160,276,9,316,95,227,250,136,186,70,315,106,221,156,247,2,131,286,196,65,210,121,237,170,80,313,145,16,262,55,200,111,242,175,85,314,150,21,266,60,46,36,41,31,26,165,317,282,126,100,191,216,290,255,76,205,116,233,180,91,312,141,11,272,51,296,365,346,355,341,331,361,336,351,375,373,162,275,6,322,97,225,251,137,187,72,321,107,220,157,245,1,132,285,197,67,212,122,235,172,82,319,147,17,260,57,202,112,240,177,87,320,152,22,265,62,47,35,42,32,27,167,323,280,127,102,192,215,292,257,77,207,117,232,182,92,318,142,12,270,52,297,367,347,357,342,332,362,337,352,377,370,163,278,7,328,98,228,252,138,188,73,327,108,223,158,248,0,133,288,198,68,213,123,239,173,83,325,148,18,263,58,203,113,243,178,88,326,153,23,268,63,48,38,43,33,28,168,329,283,128,103,193,218,293,258,78,208,118,234,183,93,324,143,13,273,53,298,368,348,358,343,333,363,338,353,378,372,161,277,5,301,96,226,254,135,185,71,302,105,222,155,246,3,130,287,195,66,211,120,238,171,81,303,146,15,261,56,201,110,241,176,86,304,151,20,267,61,45,37,40,30,25,166,300,281,125,101,190,217,291,256,75,206,115,230,181,90,305,140,10,271,50,295,366,345,356,340,330,360,335,350,376,371,164,279,8,309,99,229,253,139,189,74,311,109,224,159,249,4,134,289,199,69,214,124,236,174,84,306,149,19,264,59,204,114,244,179,89,307,154,24,269,64,49,39,44,34,29,169,310,284,129,104,194,219,294,259,79,209,119,231,184,94,308,144,14,274,54,299,369,349,359,344,334,364,339,354,379,374 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#52d4614aac36602fb386b87bb7ef7aa0910b87bb89053f8f7d172ae1bee280b9, 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 23:27:20 · history