Equation 677 Database

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Magma 281c9f5e2b98…

magma 281c9f5e2b98
Size
381
Isomorphism class hash
281c9f5e2b98ce6f924201f8f3eb6f4425dba37ada812437d454a2cb69db218b
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 23:38:42
Display reorder
380,119,129,124,114,104,109,254,259,264,269,274,279,315,316,317,312,313,314,154,159,149,139,144,134,199,204,194,214,219,209,54,294,59,64,69,74,289,29,34,49,39,44,24,284,18,9,14,4,164,169,174,179,184,189,229,234,224,244,249,239,99,299,94,84,89,79,339,334,359,344,369,353,349,364,379,374,115,125,120,111,101,106,250,255,260,266,270,275,305,303,304,302,301,300,150,155,145,136,141,131,196,201,191,210,215,205,50,291,55,61,66,71,286,25,31,46,35,41,21,281,15,6,11,1,161,166,171,175,180,185,226,231,221,241,245,235,95,295,91,80,85,75,337,330,356,341,366,350,346,360,375,370,116,126,121,110,100,105,251,256,261,267,272,277,320,318,319,323,321,322,151,156,146,135,140,130,195,200,190,211,216,206,51,290,56,60,65,70,285,26,30,45,36,40,20,280,19,7,12,2,160,165,170,176,181,186,225,230,220,240,246,236,96,296,90,81,86,76,335,331,357,340,365,351,345,361,376,371,118,128,123,113,103,108,253,258,263,268,273,278,309,310,311,306,307,308,153,158,148,138,143,133,198,203,193,213,218,208,53,293,58,63,68,73,288,28,33,48,38,43,23,283,17,8,13,3,163,168,173,178,183,188,228,233,223,243,248,238,98,298,93,83,88,78,338,333,358,343,368,352,348,363,378,373,117,127,122,112,102,107,252,257,262,265,271,276,327,328,329,324,325,326,152,157,147,137,142,132,197,202,192,212,217,207,52,292,57,62,67,72,287,27,32,47,37,42,22,282,16,5,10,0,162,167,172,177,182,187,227,232,222,242,247,237,97,297,92,82,87,77,336,332,355,342,367,354,347,362,377,372 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, M = {68} 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 23:38:43 · history