Equation 677 Database

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Magma f8f10835c371…

magma f8f10835c371
Size
381
Isomorphism class hash
f8f10835c371c983bbb903e8691bfdea067dbf90273bda3ba9ba5f45b3f43e8b
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 23:28:34
Display reorder
380,216,211,205,225,231,220,175,180,185,190,196,200,286,100,105,120,111,115,255,261,250,240,245,235,0,1,276,61,65,70,161,150,156,170,165,296,142,290,145,125,130,136,301,300,302,303,304,305,46,51,55,271,35,40,91,96,282,76,80,85,26,31,21,16,265,11,335,361,341,366,354,371,356,346,330,375,218,213,208,228,233,223,178,183,188,193,198,203,288,103,108,123,113,118,258,263,253,243,248,238,6,7,278,63,68,73,163,153,158,173,168,298,143,293,148,128,133,138,322,323,321,319,320,318,48,53,58,273,38,43,93,98,283,78,83,88,28,33,20,18,268,13,338,363,343,368,352,373,358,348,333,378,219,214,209,229,234,224,179,184,189,194,199,204,289,104,109,124,114,119,259,264,254,244,249,239,8,9,279,64,69,74,164,154,159,174,169,299,144,294,149,129,134,139,324,325,326,327,328,329,49,54,59,274,39,44,94,99,284,79,84,89,29,34,23,19,269,14,339,364,344,369,353,374,359,349,334,379,217,212,207,227,232,222,177,182,187,192,197,202,287,102,107,122,112,117,256,260,251,241,246,236,2,3,275,60,66,71,162,152,157,172,167,297,141,292,146,127,132,137,310,311,309,307,308,306,45,50,56,270,36,41,92,95,281,75,81,86,25,30,24,15,266,10,336,362,340,367,351,372,357,345,331,377,215,210,206,226,230,221,176,181,186,191,195,201,285,101,106,121,110,116,257,262,252,242,247,237,4,5,277,62,67,72,160,151,155,171,166,295,140,291,147,126,131,135,314,312,313,317,315,316,47,52,57,272,37,42,90,97,280,77,82,87,27,32,22,17,267,12,337,360,342,365,350,370,355,347,332,376 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 = {67} 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 23:28:35 · history