Equation 677 Database

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Magma 3bf4236f59de…

magma 3bf4236f59de
Size
381
Isomorphism class hash
3bf4236f59deda944b349584df92303551d28551a0591c60dbe40129cecdc7df
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 23:28:58
Display reorder
380,82,78,73,283,93,88,141,146,136,125,130,120,305,303,304,302,301,300,221,226,216,235,286,230,52,53,51,243,55,54,2,3,0,1,271,210,175,165,170,161,150,155,258,248,253,278,263,268,200,205,195,185,190,181,298,48,49,47,46,50,116,110,291,106,96,101,351,368,360,330,335,358,344,378,345,371,83,79,74,284,94,89,144,149,139,129,134,124,321,322,323,318,319,320,224,229,219,239,289,234,67,65,66,244,68,69,56,57,58,59,274,214,179,169,174,164,154,159,259,249,254,279,264,269,204,209,199,189,194,184,299,63,64,62,60,61,119,114,294,109,99,104,354,369,364,334,339,359,343,379,349,374,80,75,70,281,90,85,142,147,137,127,132,122,316,317,315,313,314,312,220,225,215,236,285,231,12,10,11,241,8,9,13,14,15,16,270,211,177,167,172,162,152,157,255,245,250,276,261,266,201,206,196,186,191,180,295,20,21,19,17,18,117,112,292,107,97,102,353,365,362,331,336,355,340,376,346,372,81,76,71,280,91,86,140,145,135,126,131,121,306,307,308,309,310,311,222,227,217,237,287,232,25,23,24,240,26,27,28,29,30,31,272,212,176,166,171,160,151,156,256,246,251,275,260,265,202,207,197,187,192,182,296,4,22,6,7,5,115,111,290,105,95,100,350,366,361,332,337,356,341,375,347,370,84,77,72,282,92,87,143,148,138,128,133,123,324,325,326,327,328,329,223,228,218,238,288,233,43,41,42,242,44,45,32,33,34,35,273,213,178,168,173,163,153,158,257,247,252,277,262,267,203,208,198,188,193,183,297,39,40,38,36,37,118,113,293,108,98,103,352,367,363,333,338,357,342,377,348,373 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {73} 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 23:28:59 · history