Equation 677 Database

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Magma 2cff68e59f7c…

magma 2cff68e59f7c
Size
381
Isomorphism class hash
2cff68e59f7c65f52bcbe5b1c78b416e5ebf58ebb44268c30e08c6ace4aa9a01
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 23:27:23
Display reorder
380,29,26,27,30,24,46,28,45,25,44,131,130,132,133,134,135,136,137,138,139,189,185,187,183,191,190,188,186,184,182,238,234,236,232,240,239,237,235,233,231,319,317,318,316,314,89,91,85,86,82,84,90,87,88,83,289,285,287,283,291,290,288,286,284,282,315,361,360,362,363,364,365,366,367,368,369,35,37,47,33,32,34,36,48,49,31,143,142,144,145,146,148,147,149,140,141,196,152,198,192,194,195,197,150,199,193,245,200,247,241,243,244,246,249,248,242,325,326,329,322,323,96,94,54,51,93,98,95,97,99,92,296,252,298,292,294,295,297,250,299,293,324,372,371,373,374,375,377,379,376,378,370,11,8,10,13,41,12,43,9,42,7,111,110,112,113,114,115,116,117,118,119,169,165,167,163,171,170,168,166,164,162,218,214,216,212,220,219,217,215,213,211,307,305,306,304,302,69,71,65,66,62,64,70,67,68,63,269,265,267,263,271,270,268,266,264,262,303,341,340,342,343,344,345,346,347,348,349,1,3,38,40,6,0,2,39,4,5,100,101,102,103,104,105,106,107,108,109,151,156,154,158,161,160,153,155,157,159,201,205,203,207,210,209,202,204,206,208,328,320,321,327,301,55,52,59,58,50,60,53,57,56,61,251,256,254,258,261,260,253,255,257,259,300,330,331,332,333,334,335,336,337,338,339,21,17,19,23,14,22,20,18,16,15,121,120,122,123,124,125,126,127,128,129,179,175,177,173,181,180,178,176,174,172,228,224,226,222,230,229,227,225,223,221,313,311,312,310,308,79,81,75,76,72,74,80,77,78,73,279,275,277,273,281,280,278,276,274,272,309,351,350,352,353,354,355,356,357,358,359 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 = {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 23:27:24 · history